It is a question of separation of Player / Character knowledge and what makes sense. The extent of RAW that we have is that you are allowed to try again, but …
Multiple capacity checks (DMG 237)
Sometimes a character fails a skill test and wants to try again. In some cases, a character is free to do so; the only real cost is the time it takes. With enough attempts and enough time, a character should finally succeed in the task.
The kicker is the section I have bolded. What does "in some cases" mean? We have no precise definition on this.
So you have to fall back on what makes sense. Think if you yourself were trying to accomplish what your character is trying to accomplish. Do you have a reason to try again? Is there any indication that you should try again?
We can assume that a dice result represents the results of your effort, not how hard you tried … so, at least, the characters know they were doing their best. Ultimately, it comes down to this: if you couldn't see the result of the dice (for example, the DM rolled for you), only the actual output of what happened, would you try again?
Let's take some examples …
Search for a room
Suppose, IRL, that you walk into a room and decide to look and see if there is a safe in the room. You search the room from top to bottom and can't find the safe. In fact, there may be a safe in the room – you just didn't think of pulling the light switch from the wall and pressing the button on the side, which would have open the hidden compartment where the safe is.
But here's the important thing … you weren't sure if there was a safe in this room. You searched the room, did your best … but you didn't "roll" high enough to find the hidden commands to reveal the safe. You have no reason to assume that you failed to find the safe, and all reason to assume that there is simply no safe over there.
On the other hand … suppose you lost your keys in your apartment. Well, you know they're there somewhere, so even if your first search "pass" in the apartment fails, you're going to try again because you're aware (or at least believe) that the thing you are looking for exists and is in the place you are looking for, so you know you have "failed" in your search, and try again.
Climb a wall
It's pretty cut and dry, honestly. You tried to climb the wall … you failed. Do you want to try O / N again?
Arts and crafts
Again, cut and dry. You did one thing … how well did you do a job? Well, you can inspect the thing you did and find out. But you may not have the equipment to try again.
It is also quite cut and dry. At the moment, did you believe this person or not? You have no clear evidence in the game to show you that your "check" was incorrect.
Again, this depends on the situation.
Suppose you follow a trail … you cross rough terrain and lose the trail. Well, you know there is a trail and the thing you are following probably hasn't ceased to exist randomly … so you might think of going back to the last place you have saw the track and try to follow it again.
However, if you look in a clearing for signs that a deer was there and you can't find any … well, you don't actually know whether or not there was a deer there, so you can't tell the difference between "missed the signs" and "no deer here". So, again, your character does not have the ability to distinguish between "failure" and "nothing here".
A bit of additional evidence to support …
While this is not directly related to skill checks, it relates in terms of a character's ability to understand how something worked, we have this bit on the invalid spell targets from Xanathar's guide to all.
If the spell normally has no effect on a target that makes a save, the invalid target seems to have made a save, even if it did not attempt one (without implying that the target creature is actually an invalid target).
So, again … as there is no clear evidence that the target was invalid … you just perceive that the spell failed to affect them. You can't tell the difference between "They've successfully backed up" and "They're immune" in the same way that, without evidence, you can't tell the difference between "I didn't drive well enough" and "There is nothing to find."
In short … think about it realistically. If you couldn't see the result of your dice, is there a clear reason for your character to know that they failed? If so, they are right to try again. Otherwise, they cannot say that they have failed.