Why would you?

I mean, I know why the player would: because they rolled a 2, and they want a better roll.

But what the roll represents is the character doing whatever search they think is reasonable under the circumstances. Otherwise they'd keep searching, right? So if they roll a 2, they not only didn't find the thing, they also don't know they've missed anything.

The circumstances may constrain what a "reasonable" search looks like. If they're searching the room while the building is on fire, maybe they should have disadvantage. Conversely, if they have unlimited time and the freedom to completely tear the room apart, then they shouldn't even roll, because the outcome isn't in doubt.

Don't fall into the trap of thinking one die roll represents one "attempt" by the character to do a task (that if they roll an Investigation check for searching for 10 minutes, they can search for another 10 minutes and roll another Investigation check). The die roll establishes a fact: that you found the thing, or you didn't.

The only case where rolling multiple Investigation checks makes sense is if they don't get to search until they're satisfied, say because someone kicks them out of the room, and they later get the chance to come back and search it some more. But how much does it matter if they find it on the first attempt or the second? If they're that desperate to find the thing, you're probably making the mistake of hiding a plot-critical item or clue behind a failable skill check. In that case I'd let the Investigation check determine whether they find it before having to leave, or they have to sneak or fight their way back in to continue searching--at which point they will find the thing, without having to roll again, because seriously?

For more on this subject, see Justin Alexander's article "Let It Ride".

Why would you?

I mean, I know why the player would: because they rolled a 2, and they want a better roll.

But what the roll represents is the character doing whatever search they think is reasonable under the circumstances. Otherwise they'd keep searching, right? So if they roll a 2, they not only didn't find the thing, they also don't know they've missed anything.

The circumstances may constrain what a "reasonable" search looks like. If they're searching the room while the building is on fire, maybe they should have disadvantage. Conversely, if they have unlimited time and the freedom to completely tear the room apart, then they shouldn't even roll, because the outcome isn't in doubt.

Don't fall into the trap of thinking one die roll represents one "attempt" by the character to do a task (that if they roll an Investigation check for searching for 10 minutes, they can search for another 10 minutes and roll another Investigation check).

• The die roll establishes a fact: that you found the thing, or you didn't.

The only case where rolling multiple Investigation checks makes sense is if they don't get to search until they're satisfied, say because someone kicks them out of the room, and they later get the chance to come back and search it some more. But how much does it matter if they find it on the first attempt or the second? If they're that desperate to find the thing, you're probably making the mistake of hiding a plot-critical item or clue behind a failable skill check. In that case I'd let the Investigation check determine whether they find it before having to leave, or they have to sneak or fight their way back in to continue searching--at which point they will find the thing, without having to roll again, because seriously?

For more on this subject, see Justin Alexander's article "Let It Ride".