Investigation is not like attacks.

Once you've investigated something, you've investigated that something to the best of your current ability.

Have you ever tried to figure out what was wrong with something? 90% of the time, after you've exhausted what you know or can try, you either find the problem or you don't.

Rolling is like looking something over and then trying everything you know or can think of.

A reroll is like trying to figure it out again, but that only has benefit if you do so after either consulting a resource, coming up with a new significant idea that lets you view the problem better or in a different way, or after getting experience with the problem or object.

In DnD that would be like either consulting with an NPC or reading a book about the subject, somehow increasing the Int attribute, or if the player can give a convincing reason why their player might be able to better investigate it a second time and not just be rehashing whatever methods they already used the first time.