I view things like stuck doors as indeterminate until a player tries to force them open. The roll isn't so much a reflection of how well the character tries, but if the door itself could even possibly be opened. I may have a door that is simply so sturdy that it cannot be broken down by human means, not that the players would know that. They can try to break it down, and I'd allow a check, but in this case it would just fail. Try again? Automatic failure.
Same thing happens if they don't roll high enough; automatic failures no matter what they roll next. The door might have been weak enough to break down, or maybe not. Once the attempt was made, it became certain whether it was or was not possible. If I run an adventure multiple times, maybe the door is strong enough in some cases, in others it's not. What I'm saying is, it's not a question of the character, but an uncertainty in the environment.
So repeated attempts simply won't work. Unless the players do something that makes it reasonable that the door was somehow weakened by some other action (such as acid in the door lock). In my mind this encourages creativity and good role playing, and that earns another attempt. (Maybe with penalty or consequences, maybe not.)
Opinions: task repetition
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