A friend of mine has a 1990 Corvette that is rarely driven in the winter. Over a period of 1 to 2 months, the battery totally discharges. This has happened for years with new and different batteries. I have other cars that can sit months with no problem. Is this a '90 Vette thing, or is there likely some short in the system? If there is a short draining the battery, how can you find it?
There is probably a parasitic drain killing the battery slowly. Finding it is usually hard and very time consuming. Most people work around it by simply disconnecting the battery when it will sit for longer than a few days.
Most likely there is excessive current draw after everything is shut down. Even a glove box light remaining ‘on’ will discharge a good battery within a few days. If there are not fuses openning, there is no short, maybe leakage but that should progress into a full blown short as soon as the insulation fries.
The best way to trouble shoot is to connect a DVM, in the ammeter mode, in series with the ground to the battery. The measured current should probably be less than 50 milliamps but check with your service manual or GM for the exact specification. If it is higher, start pulling fuses to find out which circuit is the culprit. Likely candidates are the ‘always hot’ leads to the ECM and to the radio. If nothing drops the current draw, disconnect the alternator B+ lead and see if that does the trick. If you cannot find the source of the excessive current draw, you may have to enlist the help of a auto electric technician.
Hope this helps.