Probably has the Chevrolet radio aftermarket interface that is going bad. Chevy did not have accessory power at the radio so when an aftermarket unit is installed, it requires an interface to provide an accessory power that it derives from the signals in the data stream. Many times, these interfaces go bad.

Since you have an older vehicle, I am sure you don't use Onstar (if it even has it), and I am sure it has no Bose system from the factory. So, you (or a competent shop) can just bypass the interface and run a switched accessory lead to the fuse box or body control module. You will lose the RAP (retained accessory power-supposed to leave the radio powered up even after you remove the key but only until you open the door), but most people don't care.