I'm just throwing suggestions here.
Does the camera do this only when the auxiliary battery grip is attached?
Maybe there is something up with the contacts between the grip and camera body. Try cleaning them.
I didn't have the auxiliary grip for the kit I use sometimes so am not entirely familiar with the setup but I'd try cleaning those contacts.
IDK you say power returns on it's own after sitting so...
A trip to TOCAD may be in order while you still can.