Another route
Suppose that there was a series of Papal casualties in rapid succession--a heart attack moments after uttering the Urbi et orbi blessing, oddball accidents from falling down the stairs and breaking a neck, to a gas leak somewhere, to the papal train crashing--Two or three years of five Popes in a row. Possibly no one would accept the office in the light of their god seeming unhappy with the Papacy--or perhaps the College of Cardinals would decide to leave the Papacy vacant.
For that matter, if they're dropping like flies, perhaps the pope of the week might decide that it's a sign from their god, and declare ex cathedra that changes must be made in the papacy, and that no new pope be elected until such time as changes are made.