I ran into a 'no key fob recognized' situation in my 22 4BW last week. Apparently this is possible throughout the GM line. The Fob would work actively but not passively hence you couldn't move the vehicle or operate it. The Fix is a new Body Control Module.
Here is the TSB: 21-NA-244 Chevrolet Technical Service Bulletin
Here is the TSB: 21-NA-244 Chevrolet Technical Service Bulletin