#Yes, RAW allows you to investigate the same room twice
###Multiple Ability Checks (DMG 237)
Sometimes a character fails an ability check 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 eventually succeed at the task.
It then goes on with some suggestions on how to speed things up (automatic success by taking 10 times as long), and also that no amount of time can turn an impossible task into a successful one, or that failures can sometimes make subsequent attempts harder, depending on the situation.
So yes, repeats are allowed according to RAW.