If it's a 6-speed, your problem is there is a drain when the vehicle is parked and it's not in reverse. For some reason, some of the computer functions still monitor the car even when it's shut off. Charge it, drive it, and leave it in reverse when it's parked and you shouldn't have any more problems. The same drain occurs in all of the C-6 Corvettes with a 6-speed transmission, including the Z-06's.
If it's an automatic, take it in to service, and don't worry because that's a warranty issue anyway.