A glance at http://www.catholic-hierarchy.org/bishop/sordb2.html shows that, in the whole world, there is just one single Bishop - an Archbishop Emeritus - alive today who would have been Appointed to Office and Consecrated Bishop by His Holiness Pope Ven. Pius XII.

Archbishop Bernardino, appointed on 27 April 1958. The next most senior Bishop was appointed on May 7, 1959, when the See of Peter was allegedly vacant. Pope Pius XII had taught, even in 1958 (Ad Apostolorum Principis, p. 40 etc), that Bishops receive Ordinary Jurisdiction only from the Successor of St. Peter. Bishops cannot receive Ordinary Jurisdiction when there is no Pope. The early sedevacantists always believed and said, that a false Pope cannot appoint Cardinals nor Bishops to office. 

1. Notice that +ABL relates, in an address on 8 Nov. 1979, "They (the sedevacantists) argue further that, chosen by a heretical Pope, the great majority of the cardinals are not cardinals at all and thus lacked the authority to elect another Pope. Pope John Paul I and Pope John Paul II were thus, they say, illegitimately elected." This is what cuм Ex had said also, "each and all of their words, deeds, actions and enactments, howsoever made, and anything whatsoever to which these may give rise, shall be without force and shall grant no stability whatsoever nor any right to anyone". Therefore, to neither Cardinal nor Bishop. 

So why do more recent Sedevacantists contradict earlier ones? Can a heretical Pope appoint Cardinals and Bishops to office, or not?

2. Fr. Sylvester Hunter, in Outlines of Dogmatic Theology, 1895, had already answered the absurdity of such opinions thus, "First, then, the Church is infallible when she declares what person holds the office of Pope ...This argument is in substance the same as applies to other cases of dogmatic facts. Also, it affords an answer to a much vaunted objection to the claims of the Catholic Church, put forward by writers who think that they find proof in history that the election of a certain Pope was simoniacal and invalid, and that the successor was elected by Cardinals who owed their own appointment to the simoniacal intruder; from which it is gathered that the Papacy has been vacant ever since that time. A volume might be occupied if we attempted to expose all the frailness of the argument which is supposed to lead to this startling conclusion; but it is enough to say that if the Bishops agree in recognizing a certain man as Pope, they are certainly right, for otherwise the body of the Bishops would be separated from their head, and the Divine constitution of the Church would be ruined." Clear absurdities would result from postulating vacancies over a 100 years or even longer. Why? Because false Popes cannot appoint valid Cardinals, nor can heretical Popes legitimately appoint Bishops to an episcopal office.

Every new Bishop would then only be at most an auxiliary Bishop. This would reduce the Church to a Church without Ordinaries. That is why a Sede Vacante cannot last forever. It is only a true Pope who can appoint a diocesan Bishop or Ordinary to office. All Bishops in office will die in about 60 years.

3. H.E. has a Wikipedia page, https://en.wikipedia.org/wiki/Bernardino_Pi%C3%B1era H.E. turns 104 in 5 days. At this point, 61 year SVism is clearly unsustainable. Is this supposed to be the sole Bishop with the authority to pronounce the See is vacant? That has to be done before a new alleged election, if the See were really vacant for 60 years. The Doctors and Theologians spoke at most of one single Pope becoming a heretic, and many decided even against that ever actually happening, as Our Lord Jesus had prayed, that St. Peter would not lose the faith. Not one said a series of 6 Popes for 60 years will become heretics, so that there will remain no Hierarchy with Ordinary Jurisdiction.

Maybe it's time for Traditional Catholics to move on from SVism, and regard it as a definitively falsified theory. Perhaps it's time to make the necessary efforts to work for Restoration within the Catholic Church, as the Society of St. Pius X under Rev. Fr. Pagliarani, and per the example of H.E. Bishop Fellay, is so excellently doing. "And then, from time to time, I receive letters. Like this one: I will read it to you in English because it is an image:

“Stick to your guns. Always stick to your guns.” This means: Keep your hands on your revolvers. Hold them firmly. In other words: “Defend yourselves. Always. And refuse to compromise in these matters that do not really pertain to the substance of the faith: religious liberty, ecuмenism, dialogue with non-Christian religions. There are many of us in the hierarchy who think and believe in what you are doing about these questions.” It is a bishop who wrote that to me. He does not write “I”, he writes that there are many of “us”. He wrote other things too that I dare not read to you, they are so laudatory ... “Come to our aid.” And also: “Do not let go of anything, continue like this, we need it!” This is new! There was nothing like this before! The bishops used to tell us: obviously there are problems, but at the end of the day.... And here they are telling us: “Resist, we need it!” Actually they do not speak too loud because they know very well that if they do, they will be cutting off their own heads ... I am not telling you their names because we do not want to burn out these prelates, but there are several of them.

I discover some, just like that, by surprise, and there are a certain number of them! And these are young bishops! And some of them were appointed by Pope Francis! He is not just appointing bad ones! He is all mixed up, like his whole attitude, which has also increased the general confusion. But it is extremely interesting to see that there is this movement, and I am certain that it will no longer stop. Why? Because these bishops see where the truth is, and they will not give in. They are annoyed, they are cornered, because they are in the system, but they will no longer give in. Just like these priests who have discovered the old Mass, they will do all that they can, they are annoyed, cornered, but they will keep it. These are skirmishes that have been won." http://fsspx.asia/en/content/23944

Thoughts?

When you say "Pius XII appointed bishop" you are referring to jurisdiction, which is not the main argument for sedevacantism.  +ABL, once he left new-rome, no longer had jurisdiction, yet he was still a valid and true orthodox bishop of the Church.  Same thing for +Thuc, +McKenna, +Castro Meyer and +Slepski (sp) ...and all other Trad bishops, who are the proper and only orthodox bishops of the Church today.  Orthodoxy and validity are far more important than jurisdiction, when in times of persecution and doctrinal disarray, because canon law dispenses with jurisdiction for the sanctification of souls.

But Lefebvre never claimed the modernists had no jurisdiction.

A church in which there is no hierarchy exercising ordinary jurisdiction (ecclesiavacante) is no church at all.

Xavier’s point #2 is precisely my own position, and I really don’t see how anyone could ignore Hunter’s rationale or the conclusion which follows from it.

Because false Popes cannot appoint valid Cardinals, nor can heretical Popes legitimately appoint Bishops to an episcopal office.

This gratuitous assertion is rejected by sedeprivationists.

But then you have the "Siri thesis" that Pope Casper the Friendly Ghost is floating around in hiding. He'll emerge into visibility when the time is just right. In the meantime, millions/billions of souls will have to be left on their own to falling into hell because there is no known Shepherd to guide them to salvation.

Your “shepherd” Bergoglio is doing a marvelous job guiding souls on their way to salvation. Now tell me again why you ignore his guidance? For the record, I find the Siri thesis ridiculous.

Don't assume.

Frank isn't my pope. He's an Antipope.

Don't assume.

Frank isn't my pope. He's an Antipope.

Do you believe that Ratzinger is the pope? You know, he is, in many ways, more dangerous than Bergoglio.

When you say "Pius XII appointed bishop" you are referring to jurisdiction, which is not the main argument for sedevacantism.

Yes, Pax, but we know what the arguments for sedevacantism are: the claim that the Pope is a formal heretic, and formal heretics cannot hold office. But the OP is an argument against SVism, especially 60+ year, and indefinite SVism.

Vatican I defines as Dogma that there must be Perpetual Successors to St. Peter. Svists claim 6 Popes for 60 years were all heretics. How will you reconcile 61 years of vacancy with the Vatican I dogma? Do you believe even a 100 or a 1000 year vacancy poses no problem for that dogma? As mentioned, all Bishops appointed by the last Pope cannot die. That means roughly 60 to 65 years will already be too long, because every remaining Bishop would have died or resigned.

A church in which there is no hierarchy exercising ordinary jurisdiction (ecclesiavacante) is no church at all.

Xavier’s point #2 is precisely my own position, and I really don’t see how anyone could ignore Hunter’s rationale or the conclusion which follows from it.

Yes, Sean. That's right. Though you and I disagree on SSPX-Resistance issues, we agree here that a 60+ year vacancy in the Chair is not possible. Here's the CE explain that Apostolicity of Mission and Jurisdiction is always necessary in the Universal Church, "Apostolicity is not found in any other Church. This is a necessary consequence of the unity of the Church. If there is but one true Church, and if the Catholic Church, as has just been shown, is Apostolic, the necessary inference is that no other Church is Apostolic. The history of the Catholic Church from St. Peter, the first Pontiff, to the present Head of the Church, is an evident proof of its Apostolicity, for no break can be shown in the line of succession ... All sects that reject the Episcopate, by the very fact make Apostolic succession impossible, since they destroy the channel through which the Apostolic mission is transmitted. Historically, the beginnings of all these Churches can be traced to a period long after the time of Christ and the Apostles. Regarding the Greek Church, it is sufficient to note that it lost apostolic succession by withdrawing from the jurisdiction of the lawful successors of St. Peter in the See of Rome. The same is to be said of the Anglican claims to continuity (MacLaughlin, "Divine Plan of the Church", 213; and, Newman, "Diff. of Angl.", Lecture 12.) for the very fact of separation destroys their jurisdiction. They have based their claims on the validity of orders in the Anglican Church. Anglican orders, however, have been declared invalid. But even if they were valid, the Anglican Church would not be Apostolic, for jurisdiction is essential to the Apostolicity of mission."

Well, there are different nuances in sedevacantism.  Some sedeprivationists hold that appoinments remain legitimate even when done by a Pope who only materially holds the office.

I myself hold that those so appointed can actually formally exercise office so long as they themselves do not have an impediment against doing so ... even if the appointer does.

You make it sound sometimes, Ladislaus, as if all that is necessary for a theory to be true, is for somebody to have proposed it. After someone has proposed it, it has to be proven from several authorities. Where's that proof and how many authorities have taught heretical Popes can appoint Ordinaries?

Now, beside cuм Ex, here are more authorities that go against it, Pope Ven. Pius XII: "The power of jurisdiction which is conferred directly by divine right on the Supreme Pontiff comes to bishops by that same right, but only through the successor of Peter" - if the power of jurisdiction comes to Bishops only through the Successor of Peter, then a false Pope cannot confer it, especially because the Universal Jurisdiction of the Roman Pontiff is the cause of the Particular Jurisdiction of the Bishops. Now, Ladislaus, if you believe the Universal Jurisdiction of the Roman Pontiff is lacking (when you say "the See is formally vacant") - then, if the cause is absent, the effect will not be realized.
From: http://w2.vatican.va/content/pius-xii/en/encyclicals/docuмents/hf_p-xii_enc_29061958_ad-apostolorum-principis.html para 40.

Next, here's an Encyclical of Pope Bl. Pius IX, that speaks of the necessity of the Pope for appointing or confirming Bishops to vacant sees, https://www.papalencyclicals.net/pius09/p9quartu.htm "The writings of the ancients testify that the election of Patriarchs had never been considered definite and valid without the agreement and confirmation of the Roman Pontiff ... if you consider the patriarchs of those churches which in more recent times have renounced schism and returned to Catholic unity, you will find that all of them asked for confirmation from the Roman Pontiff; the Roman Pontiffs confirmed them all by letter in such a way that at the same time the Pontiffs appointed them and placed them over their churches...We forbade the man elected to be enthroned until he received a letter of confirmation from the Apostolic See... When this is done, the Roman pontiff will choose one of those recommended and put him in charge of the vacant see."

Next Question: Supposing for a minute we grant the theory, what is to prevent an Old Catholic saying the Popes of the last 150 (or any number) years have all been heretics and thus were only "material Popes" with the See of Peter "formally vacant" all that time? How will you refute that, Lad? According to this argument, there is no limit at all in the number of material Popes we could have had, because material Popes can allegedly perform all the ministerial functions of formal Popes. You have to see that there's something wrong in that idea somewhere. You would probably tell the Old Catholic 150 years of "material Popes" is too long, or that only formal Popes can effect certain things necessary for the continuation of the Church. Right? Or if not, what would you tell such a person?

God bless.

You make it sound sometimes, Ladislaus, as if all that is necessary for a theory to be true, is for somebody to have proposed it. After someone has proposed it, it has to be proven from several authorities. Where's that proof and how many authorities have taught heretical Popes can appoint Ordinaries?

I'll provide proof of this as soon as you can provide proof that's it's permissible for Catholics to reject a General Council of the Church due to their private interpretation of Catholic doctrine and reject the Rite of Mass promulgated by the Pope as harmful to faith.  There's no "proof" for any of this.  R&R is universally rejected by all pre-Vatican II theological sources.  We're all trying to take principles and apply them, but the crisis itself is unprecedented.  Please refer to the "One Ring" thread posted by Matthew.

If you want to see the theological reasoning behind sedeprivationism, read the Cacciacuм thesis by +Guerard des Lauriers.

Those quotes of yours do not directly contradict the thesis.  As per usual, you are missing the generic distinctions.  There's significant historical and theological precedent to argue that the power of appointment or designation is materially tied to the office, while the ability to legitimately exercise it is part of the formal aspect of the power.  That's why Orthodox lines of the Apostolic Sees are considered to in fact have materially descended from those Sees, and the Church doesn't try to fill those Patriarchates.