If you have a short in the harness or a low battery it'll slowly kill the alternator. Check the voltage on the battery with the car off, the voltage when the car is idling and the voltage when the car is at ~2500-3000 rpm. The alternator and battery work as a team; if one has a problem they can both be damaged.
Also test continuity or resistance from the alt case to cyl head to ground studs. They all should be virtually 0 ohms. The e30 motor ground strap tends to decay internally - it carries a lot of amps. It's on the driver's side at the motor mount. Check that for resistance if you see anything odd.
Alternatively, take the battery and alt to (at least two) parts stores and get them tested. Those dynamic tests are the most reliable information you can get. They'll do it for free (and sometimes give really good advice).