There is, of course, a more mundane reason why some Catholics, including some in the Vatican, don't want the pope to resign. Those who favor his policies want them to continue, and those whose jobs depend upon his tenure don't want to be out of work.

What would happen if the pope became incapacitated?
At one level, this question can be phrased in terms of John Paul's health care: How far would physicians go to keep the pope alive, should he slip into a coma or persistence vegetative state? Catholic moral teaching holds that ordinary treatment is obligatory, "extraordinary means" are not, but leaves open precisely what constitutes "extraordinary means." While it seems the pope has not left behind any specific directives on the question, he did send a message a year ago to a Rome conference on the care of patients in these circumstances: "The sick person in a vegetative state, awaiting recovery or a natural end, still has the right to basic health care (nutrition, hydration, cleanliness, warmth, etc.), and to the prevention of complications related to his confinement to bed. He also has the right to appropriate rehabilitative care and to be monitored for clinical signs of eventual recovery. . I should like particularly to underline how the administration of water and food, even when provided by artificial means, always represents a natural means of preserving life, not a medical act. Its use, furthermore, should be considered, in principle, ordinary and proportionate, and as such morally obligatory, insofar as and until it is seen to have attained its proper finality, which in the present case consists in providing nourishment to the patient and alleviation of his suffering.
" Since this is the closest thing to an expression of the pope's wishes, it seems likely physicians would feel obliged to honor it. In an Feb. 25 interview with CNN, Cardinal Jorge Medina Estévez, a Chilean and former head of the Congregation for Divine Worship, and currently the cardinal in line to make the announcement of a new pope in St. Peter's Square, said that the use of "extraordinary means" to some extent depends on the specific person -- "on the role of this person in his family, in society." Medina added that the use of an artificial respirator today would not constitute "extraordinary means." All this seems to suggest that if the pope ever arrived in such a condition, the Vatican consensus would be to prolong his life as much as possible through use of standard medical technology and the administration of food and water. The other level on which the incapacitation question occurs is church governance, and there the waters are considerably murkier. Canon law makes no provision for the removal of a pope except through his own free choice to resign, exercised in the moment. Without a pope able to give assent to decisions for an extended period of time, bishops could not be appointed and teaching documents on faith and morals could not be issued. The long-term risk would be paralysis. Commentators from a wide variety of points of view, such as the liberal Fr. Richard McBrien and the conservative Michael Novak, concur that this represents a "hole" in church law. There's general agreement that this legal gap is unlikely to be filled now, since it would seem like a maneuver to depose John Paul.
This may well be one of the first tasks awaiting the next pope - appointing a blue-ribbon panel of canon lawyers and experts on the papacy to work out a system for declaring the See of Peter vacant.

What might happen in the meantime if we get to this point? The initial impulse would be to continue routine church business along the lines already indicated by the pope, deferring new challenges. How long that strategy would work against the force of changing circumstances, especially the need for bishops in dioceses, is impossible to predict.