In RC theology it actually is promised to the office, at least when speaking according to V1 conditions. However,
Although the individual bishops do not enjoy the prerogative of infallibility, they nevertheless proclaim Christ's doctrine infallibly whenever, even though dispersed through the world, but still maintaining the bond of communion among themselves and with the successor of Peter, and authentically teaching matters of faith and morals, they are in agreement on one position as definitively to be held.(40*) This is even more clearly verified when, gathered together in an ecumenical council, they are teachers and judges of faith and morals for the universal Church, whose definitions must be adhered to with the submission of faith.(41*)
Yet,
The degree in which the infallible magisterium of the Holy See is committed must be judged from the circumstances, and from the language used in the particular case. — Catholic Encyclopedia>Encyclical; http://www.newadvent.org/cathen/05413a.htm Moreover,
Bishops, teaching in communion with the Roman Pontiff, are to be respected by all as witnesses to divine and Catholic truth. In matters of faith and morals, the bishops speak in the name of Christ and the faithful are to accept their teaching and adhere to it with a religious assent. This religious submission of mind and will [versus assent of faith which infallible decrees require] must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; — http://www.vatican.va/archive/hist_councils/ii_vatican_council/documents/vat-ii_const_19641121_lumen-gentium_en.html
Still,
Donum Veritatis also allows that even if "not habitually mistaken in its prudential judgments," "some Magisterial documents might not be free from all deficiencies," and withholding assent is allowed for a theologian "who might have serious difficulties, for reasons which appear to him wellfounded, in accepting a non-irreformable magisterial teaching." In such "even if the doctrine of the faith is not in question, the theologian will not present his own opinions or divergent hypotheses as though they were non-arguable conclusions..." - https://en.wikipedia.org/wiki/Obsequium_religiosum
Guess how many variant RC opinions there are on this?
However, the premise of ensured perpetual magisterial infallibility as per Rome (and basically in primary cults) is a unScriptural novelty.
. . . with the successor of Peter . . . (my bolding for emphasis)