Seems like a valid argument,  but I'm not a theologian...
I'm also not a sedevacantist, so defective pope is easier to stomach than no pope.

Can someone explain how this theory of sedeprivationism differs from the classic SSPX R&R position?

Anyway, it sounds like a novelty. The devil loves novelty. It's actually an easy way to spot heresy.

From the above article, I think summarizing the various positions:

In the Present Crisis of the Church:

1.) The Pope preserves his Pontifical authority which is divinely assisted.

11. And one should submit to his disciplinary decisions, while at same time denouncing the doctrinal errors of his teaching and his personal responsibility for them (CRC).

12. But one should not submit to his disciplinary dispositions. It is necessary to transmit the Sacraments and the Faith against his authority ("ECONE").

2.) He no longer has his divinely assisted Pontifical authority.

21. He is deposed because of his personal heresy. ("Sedevacantism")

22. But he is not yet deposed: he materially occupies the Apostolic throne. ("Thesis of Cassiciacuм")

And continues:

As can be seen, the Thesis of Cassiciacuм is completely different from those theses which proclaim that Authority continues to exist in those who occupy the Apostolic See, and from those who claim that Paul VI and John Paul II are pure and simply deposed, that they are anti-popes and that the See is vacant.

The Thesis of Cassiciacuм can restated in the following manner: Since December 7, 1965 (the reasons for our specifying this particular date will become clear later), the person occupying the Apostolic See is no longer formally the pope: He no longer has any divinely assisted Pontifical authority; he however remains materially a pope insofar as he has not been juridically deposed.

The distinction between thesis 21 and 22 (referring to the above chart) can give rise, on first sight, to the classic debate on the problem of a heretical pope: is he depositus or deponendus?[4]

This juxtaposition is however inadequate.

The first and most important reason is that the Thesis of Cassiciacuм does not appeal to any preexisting theory on the problem of an heretical pope. It remains apart from the debate. As we shall see, this is what gives it force and allows it to establish, in its essential elements, independent of open theological discussion, something approaching a certitude of the order of the Faith.

The second reason is that the Thesis of Cassiciacuм which says the occupant of the See is not deposed, does not ABSOLUTELY say he should be deposed. It only says this hypothetically: he should be compelled (by the Catholic bishops and by the cardinals, or by any competent Authority in the Church) to condemn the errors; it is only after such an official demand is made on the part of those who have Authority in the Church that deposition can occur: that is to say, when the occupant of the Apostolic Throne refuses to confess the Faith and condemn the errors contradicting it. (Only then could the Bishops and or cardinals officially state that he is deposed, the person responsible for deposing him being Christ.) But, should the occupant of the Throne comply with the demand: then his act of condemning the errors would ipso facto establish him as being formally the Pope.

Cantarella - Privationism argues and practices that the pope is no longer divinely assisted.  R&R argues and practices the opposite.  That's a big difference!  In practice, a huge burden is lifted from the shoulder of traditionalists who cannot stomach the thought of a having garage pope.  Also, the devil loves chaos.  Look at the chaos the new saint factory has created.  This makes R&R stand out like a sore thumb.

s2srea - thanks for that little chart summary.  

mithrandylan - You sow cockle.  A idea of a material pope is found in catholic theology(the very fact of our differences support it).  A material and entirely in potentia church is not.  Don't twist things or use Fr. Sanborn as our spokesman.  

Sedeprivationism is intellectually rigorous, and a worthy effort, but I don't think it answers the great difficulties that simple sedevacantism raises, and which it was devised to resolve.

Sedeprivationists would need to cite a traditional source justifying their division of authority or jurisdiction into a composite having matter and form, because typically authority is not divided in such a way. To possess an office is to possess the authority or jurisdiction attached to it, there is nothing else beside it to possess. He who does not possess authority over a particular flock, who does not stand in a habitual relationship over them, does not possess the office in any way, not even materially.

Jurisdiction is in its essence, as all canonists and theologians explain, a relationship between a superior who rules and a subject, or flock, who is ruled, the one standing in a real metaphysical relationship over the other within the Mystical Body. But if this is lacking, in what sense precisely is the material occupant still an occupant of the see?

It is said the Popes retain only the material element of the Papacy, which is the title and designation, but lack the formal component, which is the authority and jurisdiction, a distinction that was not traditionally made.

Granting this for now, for argument's sake. Then, it is claimed that these "material Popes" can designate others, such as electors and even bishop-designates.

So, the two questions of the greatest import are - can the "material Pope" really designate Cardinals, can he appoint Ordinaries to other sees of authority?

Fr. (later Bp.) Lauriers was the principal expositor of this thesis, but its leading exponent today is Bp. Sanborn - this is what he writes,

"This right of designating, which is found in Paul VI or in John Paul II does not constitute them as popes, because they lack authority or the right of making law. Therefore they are not popes except materially. They can, nevertheless, designate electors and even bishops for the purpose of succeeding to sees of authority"

This thesis is very complicated and therefore its refutation will correspondingly be such as well - the brief answer is this - the traditional doctrine is this, when a Pope appoints a bishop, it is his Papal power, the universal jurisdiction that he possesses in act, that effects the transmission of particular jurisdiction onto the bishop. But if sedeprivationists deny the Pope his universal jurisdiction, then the bishops he appoints will not have particular jurisdiction, for the cause is lacking, the effect cannot be realized. The bishops he appoints, as some sedeprivationists concede, will also just be mere material occupants of their episcopal sees. But in this case formal Apostolic succession will cease, because formal Apostolic succession requires the transmission of the ordinary power of jurisdiction.

Will a Pope designate be able to designate Cardinals? It may be doubted. For Cardinals receive the right of election because, as their name suggests, they are incardinated into the Roman Church, enabling the Petrine succession to continue. Now, incardination is an act where one cleric is transferred from the jurisdiction of one bishop to that of another (see http://www.newadvent.org/cathen/07704a.htm ), to henceforth stand in a habitual relationship to the bishop of the place where he is newly incardinated, in this case the diocese of Rome. But if this habitual jurisdiction and it precisely is lacking, how is the act of incardination to be effected? In this case, the Cardinal will not then receive the power of designation, because he will not be incardinated into the Roman Church, where the power prinicipally resides.

These, briefly, are some of the critiques non-sedeprivationists have made of the thesis. Undoubtedly it is a serious effort to make sense of a difficult situation, but ultimately an unsuccessful one.

Sedeprivationism makes the most sense to me. It would explain how God is not allowing His Church to go through years and years without a Pope. It would also explain how a Canonization of someone like Padre Pio could be legit while the fake canonizations of JPII and John XXIII are not. It's really the only option that makes sense to me.

To the bolded part, not really. It is the pontifical power that is the cause of infallibility in the act of canonization. If that is lacking, then all of these canonizations are invalid, and would one day have to be made again by a Pope who possesses real authority, in order for them to be infallibly certain. Hence when Vatican I is explaining the matter, it says "in the exercise of his office ... by the divine assistance promised to him in blessed Peter" showing what is the cause of infallibility.

On that matter, sedeprivationists are no different from simple sedevacantists, and its adherents frankly say so. The claim is that sedeprivationism allows the Apostolic and Petrine succession to be perpetuated, whether that is actually correct is another matter altogether.