question of whether to resign
Used when someone's continued tenure is in doubt, typically in political, corporate, or organizational contexts.
The question of whether the minister should resign is being discussed.
進退 means 'advancing or retreating' or 'course of action', while 進退問題 specifically refers to the issue of resignation.
Compound of 進退 (advance or retreat; course of action) and 問題 (problem, question).