In a stack on a POP we want to delete the last inserted element.
So, here keys chosen are in strictly decreasing order, so that when you want to pop, and call deletemin(), it will delete element with lowest key, which is last inserted, and that is what we want.
If keys chosen are decreasing but not strictly decreasing (repetitions can come), then for keys with same values, the first inserted element will be deleted first (priority queue becomes a normal queue for keys with same values) and this is not what we want in a stack.