I'm wondering if there is anything that would prohibit an investigator from performing the same action twice? I didn't notice anything in the rules.

Yes, an investigator may perform the same action twice. From the RRG p. 4:

During an investigator’s turn, he performs up to two actions.

An investigator can perform the same action more than once per round.

During an investigator's turn, he performs move action one or time ?

An investigator may perform one move action per action slot he has available that turn. This means that normally you're allowed to perform up to two movement action / turn, and each movement action allows you to move up to two spaces

The only exception to this is a particular Insane card that specifically prevents an investigator from doing two of the same action in a turn. That makes it particularly difficult if one needs to run.