Can you name any bishops from the time of Bellarmine until today who the Church recognizes as having lost their office for heresy, before the crime had been legally determined by the Church?

    The theory, which holds that the pope, while still in office, can be judged and deposed for heresy; whether the deposition be considered as a proper act of juridical deposition, or as an act of removal of one who is considered jure divino removable upon having been judged guilty of the crime of heresy by competent ecclesiastical authority, and as a consequence of that judgment to have fallen from office ipso facto; has, since the time shortly after the First Vatican Council, been unanimously rejected by theologians, since it could be clearly seen, in the light of the absolute supremacy and injudicability of the pope set forth in solemn definition of the primacy, to be contrary to the faith of the Church. Likewise, the belief that a true and valid pope could even fall into formal heresy was generally abandoned after Pastor Aeternus taught that St. Peter and his successors were given the grace of unfailing faith as a requisite disposition for exercising the charism of papal infallibility. St. Robert Bellarmine had also forcefully argued this point in Caput iii Liber iv of De Romano Pontifice; but it was only after the support it received from Pastor Aeternus, that Bellarmine’s position on the question became the opinio communissima.  Since then it has been the nearly unanimous opinion of theologians that a pope cannot fall into formal heresy. While in the Middle Ages it was the far more common opinion among theologians and canonists that a pope could fall into formal heresy, and that he could be judged for heresy by a council; conversely, by the time of the Tridentine and post-Tridentine period, the great Counter-Reformation doctors such as Cajetan, Bellarmine, Suarez, and John of St. Thomas, were of the opinion that a pope cannot become a formal heretic, and therefore considered the question of papal heresy as a mere hypothesis.
    Today, more than a century after the opinion that a heretical pope could be judged while still holding office and deposed by the Church had been discarded and totally abandoned by theologians, since that opinion was clearly seen to oppose the dogmatic pronouncements of the magisterium; that opinion has resurfaced in some quarters, due to the doctrinal heterodoxy of the “Conciliar Popes” – i.e. the popes, beginning with John XXIII up to the present, who have all, without exception, distinguished themselves in the most dubious manner but in different degrees – having deviated from the rule of faith in their opinions and pronouncements. It is due, in no small measure, to the deceptive sophistry of the Conciliar Church propagandists, John Salza and Robert Siscoe, that this heretical opinion, which holds that a pope while still in office can be judged by his inferiors in the Church, has experienced a recrudescence; and ironically, it is in the sector of the Church where the most careful attention to doctrinal rectitude is usually found, i.e. among the traditionalists, that this errant theory, which can be seen to be heretical in the light of Pastor Aeternus, has been resurrected.
    In his book, Contra Cekadam, the learned and highly respected rector of the Hearts of Jesus and Mary Seminary, Fr. François Chazal, has adopted the opinion of John of St. Thomas on the question of deposition of a manifest heretic pope from office. It was the opinion of John of St. Thomas that one who is manifestly a formal heretic would not fall from the papal office ipso facto; but would remain in office as pope until convicted of heresy by a council, and then would only fall from office upon being declared vitandus by the council. This is the fourth of the five opinions outlined by St. Robert Bellarmine in Book II of his De Romano Pontifice. Bellarmine utterly demolished this opinion in his refutation of it in chapter 30, and his own opinion (the fifth opinion) that a manifest heretic pope would straightaway fall from office ipso facto, was eventually incorporated into the 1917 Code of Canon Law (Canon 188 n. 4); and remains in force in the 1983 Code. According to Canon 188 n. 4, one who publicly defects from the faith automatically falls from whatsoever office ipso jure. In this volume I have demonstrated that this position is indeed, as Bellarmine called it, “the true opinion” beyond all shadow of doubt, and beyond any legitimate dispute.  
     Unfortunately, since Fr. Chazal is refuting a sedevacantist in his work, he relies too heavily on the thoroughly dishonest scholarship of Salza & Siscoe in their fraudulent diatribe against Sedevacantism, True or False Pope? This unfortunate reliance, which is undoubtedly due to its being the most exhaustive exposition published on Sedevacantism to date, is plainly discernible in Bishop Richard Williamson’s comments on Fr. Chazal’s brief work.

The Church Militant is a juridical institution with a spiritual aspect, not a spiritual entity with an juridical aspect.  

Interior faith is, according to one opinion (e.g. Franzilin, Garrigou-Lagrange), necessary to be member of the Church secundum quid, but not simpliciter, while according to the more common opinion (e.g., Bellarmine, Billot) it is in no way necessary for membership.  But according to both opinions, interior faith is not required for a person to legitimately hold office in the Church, since holding office pertain to the Church as a visible, juridical society.

Similarly, to lose an ecclesiastical office for heresy, the culprit must be guilty of the crime of heresy, since only the crime separates a person from the Church juridically.  


Wernz-Vidal: “a General Council declares the fact that a crime had been committed, a crime by which the heretical pope on his own had separated himself from the Church..” (Wernz, Ius Decretalium, 1913, II, p. 615).

If the sin of heresy resulted in the loss of office, how would you ever know who legitimately held office? and how could the Church ever declare that an office had been lost for heresy, without being able to read hearts?  

But I do agree with you that Fr. Kramer contradicts himself when he says a pope cannot lose the faith, and then says if Francis were the true Pope, he would have lost his office for heresy.  If you read Fr. Kramer's arguments carefully, you find similar contradictions constantly.

Except Fr. Kramer and Fr. Chazal disagree on who is the pope. Not an insignificant matter.

Funny how you cite Bellarmine while you completely ignore his writings refuting the belief that a heretic Pope could retain the form of his office until deposition. In fact, he went so far as to say that the belief a manifest heretic Pope is not ipso facto deposed "cannot be defended". He addressed the "secundum quid vs simpliciter" distinction too.
http://www.cmri.org/02-bellarmine-roman-pontiff.html

Obviously it's to his judgement. Everything a man says is to his own judgement. I never claimed Bellarmine was infallible.