Who investigates businesses that operate on post?

SFC (Join to see) Your Tag line "Who Investigates Businesses" is grossly out of touch with your observations and reasoning provided " food businesses closed when soldiers are off, businesses closed unreasonably early and in general businesses on base that are just leeches on our military."
"Investigations" would be done by CID, but that does not apply to the business and the issues you mentioned.

You are unhappy with the business practices of a business on post, fair enough. Choose not to do business with them, if enough like-minded people do the same the business will quickly leave. It is not cheap nor easy to operate a business on post. If customers are not coming through the door and paying for goods and services, the doors will shut.

If you still feel the need to make a complaint..may I suggest you speak to the owner of the business, perhaps you will learn something, perhaps the owner will learn something.
If you already have, are unwilling or unable to speak with the offending business owner your action agency is AAFES. You can do that through an ICE complaint, or go directly to AAFES https://www.aafes.com/about-exchange/doing-business/quality-assurance/customer-complaints.htm
But just like the IG will always go to the commander first, AAFES will always go to the business first so you might as well start there.

Ultimate responsibility lies with the base commander with the exchange manager acting as a quasi staff officer.

I have found the IG to be extremely helpful in resolving issues negatively impacting soldiers SFC (Join to see). It could be a place to start and if it’s not in their jurisdiction, I feel certain they would know in which direction to point you! Good Luck!