You might look at the charging system as that has given GM owners a real lot of problems since they redesigned their generator for the 1987 model year. The system should be checked for maximum current output and for "ripple" along with charging voltage.
If all you can get is one third of the typical rated 90 to 120 amps, ripple will also be very high. Those are signs of one failed diode of the six.
The voltage regulator is a high failure item too. Both that and the diodes are destroyed by the huge voltage spikes these generators produce, and low voltage and / or high ripple wreaks havoc on the many computers on the vehicle. It's common to go through four to six replacement generators in the life of the vehicle, and the best way to reduce the number of repeat failures is to replace the perfectly good battery at the same time unless it's less than about two years old. As they age they lose their ability to dampen and absorb those spikes.
What you're describing is one of the common symptoms of a charging system problem. Rule that out first, then go looking for some less-likely cause if necessary.