I'm an old school guy, so I don't like the standard rule on repeated checks. It tends to make some tasks meaningless, since you can just always succeed against a DC of 20 or less (assuming you don't have a negative modifier), such as getting out of manacles or picking locks. 3E tried to solve this by making the DCs very high (usually above 20), but this had the negative effect of making a single attempt very unlikely to succeed. Given that in 5E, DC 20 is supposed to be a "hard" task, and that bounded accuracy keeps the DCs lower (manacles are DC 20 and locks are DC15 standard), this makes them pointless unless the DM has set an arbitrary time limit.
Instead, I consider the roll to be the character's best effort at succeeding any any given task under those conditions, making rechecks impossible. For example, you attempt to break free of the manacles and fail, then you just can't do it unless something changes the situation. If the manacles are damaged in someway (such as you taking fire, cold, acid, etc. damage), then another check would be allowed, because the manacles might have been weakened. If something might give you a massive adrenaline surge (such as the BBEG holding you prisoner threatens a loved one), I might allow another check.
Sometimes there are things that may look like rechecks, but are not. For example, if you try to force a stuck door open but fail, you can still break it down over time by hitting it with weapons (item HP & AC), and I may not bother making the attacks because you'll eventually succeed. These usually have other consequences however, such as the door now being destroyed, rather than just open (plus you probably made a lot of noise). Basically, if you fail the check, there may be another way to do what you need to do, but with consequences.
Instead, I consider the roll to be the character's best effort at succeeding any any given task under those conditions, making rechecks impossible. For example, you attempt to break free of the manacles and fail, then you just can't do it unless something changes the situation. If the manacles are damaged in someway (such as you taking fire, cold, acid, etc. damage), then another check would be allowed, because the manacles might have been weakened. If something might give you a massive adrenaline surge (such as the BBEG holding you prisoner threatens a loved one), I might allow another check.
Sometimes there are things that may look like rechecks, but are not. For example, if you try to force a stuck door open but fail, you can still break it down over time by hitting it with weapons (item HP & AC), and I may not bother making the attacks because you'll eventually succeed. These usually have other consequences however, such as the door now being destroyed, rather than just open (plus you probably made a lot of noise). Basically, if you fail the check, there may be another way to do what you need to do, but with consequences.