No, in general.
There's nothing ever stopping someone declaring a retry of an action, just like there's nothing ever stopping someone declaring (an attempt at) something impossible as an action. There may be many things, however, that cause those declarations to be useless endeavours and-or wastes of time; but that alone does not prevent those declarations from being made either in jest or as serious things.
In most games I run, whether it’s D&D or something else, I don’t allow second attempts as you’ve described. In D&D, I similarly don't allow multiple players to roll for their characters. The group essentially gets one roll, and if anyone else can help, then they roll with advantage. The result of that roll determines the outcome.
If we’re in a situation where multiple rolls seem like they’d make sense… like being at a locked door for over a day… then I simply grant success without a roll. Or I ask for a roll and use that to determine how much time it takes, rather than success or failure.
Obviously, there are different ways to handle this.
Well, again, this is highly dependent on the kind of process of play and overall structure of the game you are playing. Such a statement won't make much sense in the context of Dungeon World for instance, were the idea of 'retrying' something is very unlikely to come up.
Yup. At least not without something significantly changing in the fiction.
In my home group’s second Stonetop session, our Lightbearer tried to set up a distraction for some crinwin (the setting’s low-level kind of goblin type critter) to allow for a quick getaway past some nests the group had come across in the forest. He tried to use an incantation but rolled poorly, so before he was able to finish, crinwin began pouring from the nests and swarming toward him.
I asked what he wanted to do. He said he wanted to try again. I said there’s a group of eight that are almost to you. Some of them will reach you no matter what, so you’ll take some damage regardless. If the roll goes poorly, then you’ll take more damage and some kind of harm as well. The way damage works in the game, he was facing 1d6+7 hit points at least, and currently had 10 hit points. Death was very likely on the line.
He decided to go for it. Luckily, one of his buddies the Ranger, was able to act and fired a hail of arrows that reduced the number of incoming crinwin, which greatly reduced the damage the Lightbearer faced.
He wound up rolling well, and took only 5 points of damage before his incantation worked and the crinwin were mesmerized by his light.
I almost didn’t allow a second attempt, but given the circumstances and how the danger had been established, I thought this was a good way to handle it.
My point is that even there, there's nothing at all stopping the player from declaring "I try again", even if the act is already meta-known to be futile.
I mean, set the whole notion of meta aside. Just tell the player “it’s futile and the thief knows it is” and then get on with the game.