Precisely because of what your experience I always play with the timer on. I was defending Constantinople (playing as the Turks, sorry) against four stacks. Three of them were normal armies and one was a lonely general (either the king of Hungary or the German Emperor I don't remember). The enemy managed to breach the gate with the second ram (out of four). I defended a breached gate against the three stacks and after that my units were depleted and exhausted. The general was all that was left. Since the gate was breached all he should do was march and attack my exhausted men. He stood still and apparently was stuck by a rock. Although he shouted orders to advance his unit didn't move. My archers had now arrows left and I couldn't reach him with my spears. Since I couldn't kill him the battle couldn''t end. This battle had lasted four two hours and now I couldn't end it.
It was very late in the evening so I quit end reloaded a save game and did auto_win defender. Since that battle I always leave the timer on.