Electrical problems with 95 325is

I have a 95 325is that is having electrical issues. I was driving one day and the warning lights on the dash began to light up one after another, and soon the car shut down and wouldn't restart. Turned out to be a bad battery. It ran fine with a new battery for several days then the same thing happened. The shop (not a BMW shop though) checked it out and couldn't find anything wrong with it, but the same thing happened again. The alternator checked out fine. Could this be due to a short circuit somewhere or could it be something else? Any help is appreciated.