One Pope good, two Popes...?

The Pope's decision to resign is likely to create problems for Catholic theologians. Dogma says that the Pope is infallible when making pronouncements ex cathedra (that is, in the exercise of his office) on matters of faith.  The question is, does that infallibility magically cease if he resigns?  I think it would be difficult to argue that you can be infallible one minute and not the next - and in any event, dogma says that a Pope is chosen by God, and therefore only God can remove him. The current Pope is known to be a traditionalist - suppose his successor is a moderniser, and decides to relax the Church's views on contraception, say.  Even if Benedict hides himself away somewhere, he is bound to become a focal point for conservatives who want to keep things as they are - and who will have the high ground on infallibility?  You can see the problem.