Can the Pope Become a Heretic as a Private Doctor?

There are two schools of thought on this question.

The first school, says that a Pope can become a heretic:

S. B. Smith in his Elements of Ecclesiastical Law, written prior to the promulgation of the Code of Canon Law states: “Q. Is a Pope who falls into heresy deprived, ipso jure, of the Pontificate?  A. There are two opinions: one holds that he is by virtue of divine appointment, divested ipso facto, of the Pontificate; the other, that he is, jure divino, only removable.  Both opinions agree that he must at least be declared guilty of heresy by the church-i.e., by an ecumenical council or the College of Cardinals.  The question is hypothetical rather than practical.  For although, according to the more probable opinion, the Pope may fall into heresy and err in matters of faith, as a private person, yet it is also universally admitted that no Pope ever did fall into heresy, even as a private doctor.”

“Should the Pope as a private person fall into heresy, publicly and notoriously, he would place himself outside of the Church and ipso facto lose his office.”  (Wernz. II, n. 614.)  Constitution of the Church by Ayrinhac (1925).
Dogmatic Theology: Christ’s Church by Van Noort (1957) teaches: “All theologians admit that the pope can make a mistake in matters of faith or morals when so speaking: either by proposing a false opinion in a matter not yet defined, or by innocently differing from some doctrine already defined. Theologians disagree, however, over the question of whether the pope can become a formal heretic by stubbornly clinging to at error in a matter already defined. The more probable and respectful opinion, followed by Suarez, Bellarmine and many others, holds that just as God has not till this day ever permitted such a thing to happen, so too He will never permit a pope to become a formal and public heretic. Still, some competent theologians do concede that the pope when not speaking ex cathedra could fall into formal heresy. They add that should such a case of public papal heresy occur, the pope, either by the very deed itself or at least by a subsequent decision of an ecumenical council, would by divine law forfeit his jurisdiction. Obviously a man could not continue to be the head of the Church if he ceased to be even a member of the Church.”

And Against:

Michael Davies quotes de Romano Pontifice of Saint Robert Cardinal Bellarmine (An Heretical Pope): “This opinion (that the Pope could not become an heretic) is probable and easily defended … Nonetheless, in view of the fact that this is not certain, and that the common opinion is the opposite one, it is useful to examine the solution to this question, within the hypothesis that the Pope can be an heretic.”  Davies goes on to state: “The great Jesuit theologian, Francisco de Suarez (1548-1617) was also sure that God’s “sweet providence” would never allow the one who could not teach error to fall into error, and that this was guaranteed by the promise Ego auten rogavi pro te … (Luke 22:32).”  He goes on to quote Saint Alphonsus Ligouri: “We ought rightly to presume as Cardinal Bellarmine declares, that God will never let it happen that a Roman Pontiff, even as a private person, becomes a public heretic or an occult heretic.”

Andre Perlant in An Papa Hereticus Deponi Potest also confirms that Bellarmine thought that it was impossible for a Pope to become a heretic.  He however, quoted the other proposition and has been quoted from, but OUT OF CONTEXT.  Perlant reports that Bellarmine went into every case of alleged Papal heresy and disproved them all, confirming what has been reported above that this has never happened in the past.