Suppose a creature succeed on a Stealth check to hide, say, in a brake. Suppose also the brake is large enough to move within it (100 × 100 feet, for example). If a creature wants to make a move and/or take a Dash action while remaining in the brake, does it need to re-roll its Stealth check? If yes, then when has it to re-roll (before the move, or after?) and how often (every turn of moving, with every move and every Dash action separately, etc.)? Also, what kind of action does this check take (an action, a bonus action, etc.)?
Until you are discovered or you stop hiding, that check’s total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence.
Hiding (as a verb) means "To keep oneself out of sight or notice" - it is not inherent in this definition that you cannot move or take any other action. Indeed the skill is called Stealth which means "The act of moving, proceeding, or acting in a covert way". It is entirely reasonable to "hide" in plain sight if the intent is not to be noticed rather than not be seen.
The only ways that a character ceases to be hidden is if somebody finds them (and communicates this to others who have not found them) by beating the Dexterity (Stealth) check with a Wisdom (Perception) check or if the character "stop[s] hiding" - a conscious choice. A new Dexterity (Stealth) check is only called for when you want to hide again after being discovered or circumstances change such that your method of hiding is no longer appropriate (e.g. you were hiding in a crowd which disperses, you move from a paved area to an area covered with fallen branches and leaves) or you engage in an activity which clearly increases your chance of being noticed (e.g. running with the Dash action).
Doing otherwise will simply result in the character failing eventually. For example a character with +5 to Dexterity (Stealth) facing an opponent with a 10 passive Wisdom (Perception) will succeed 75% with one roll, 56% will 2 rolls, 42% with 3 and only 32% with 4. This is an unfair nerfing of a skill the player chose over another skill - does the DM require multiple Intelligence (Investigation) checks to find a secret door, multiple Dexterity (Athletics) checks to jump a chasm, or multiple Wisdom (Perception) checks to find someone who is hidden? The Alexandrian has an excellent article on this.
See these related questions:
- What advantages does hiding have?
- How does the Stealth versus Perception check work in combat?
- Sneaking through areas people are watching closely
- Group hide and seek
- How to cope with bad rolls on important actions?
- How do I make sure that both passive and active perception stay relevant?
- I rolled a 20 on a stealth check. What now?
If your DM says "make a Stealth check", you have to roll
As a player, you roll dice only (and every time) when a DM says "make a X check". When do you need to roll and how often that happens is up to the DMing style their use. For more info see the DMG page 236 - "The Role of Dice".
The rules don't say much about Stealth mechanics
when has it to re-roll (before the move, or after?) and how often (every turn of moving, with every move and every Dash action separately, etc.)
If you're the DM, you should listen to Jeremy Crawford in the corresponding podcast (08:58 – Sage Advice – Stealth). Basically he says that in 5e all Stealth checks are up to the DM by design (because 3.5 was a bad stealth simulator, and they tried to address that issue in 5). It is the DM's job to decide, how to resolve all kind of hiding actions, when and what skill checks to use. As a DM, if you need more specific instructions regarding skill checks, consider using a stricter rules system, like Pathfinder.
If you're the DM, keep in mind these things:
- You don't have to ask for a roll. A character can automatically fail the hiding attempt if he is not stealthy enough (for DM's discretion). For instance, if they shout aloud in the brake, they probably will be noticed regardless of the preceding roll.
- Asking for a check, you can (and should) apply situational (dis)advantage. If you think the Dash action should spoil the hiding, ask for another roll with disadvantage. If the brake has a lot of vegetation to hide in, apply advantage (or do not ask for another roll at all). Use common sense. It is your job to make the situation feel more "real".
- Since a single failed check will spoil the hiding place, the more rolls do you ask, the more dangerous situation becomes for the hiding character. If you think a player shouldn't be found (for the sake of the plot or whatever), don't ask for additional checks.