Cold Weather Arrives, Car Dies

I have a well-maintained 1999 Mustang coupe with 79,000 miles on it. When the weather turned cold in late fall of 2008, the battery began dying for absolutely no apparent reason. This happened about 10 times, in irregular intervals, over the course of 5 months. Other than the cold temperatures, there was no pattern to this. The battery was replaced twice and the alternator once. After the alternator replacement in early March, I had no further problems until last week. Temps here dropped into teens and 20’s, and my husband went out to start the car one morning, only to find the battery so drained that he couldn’t even open the car with the keyfob. My beloved red Mustang has now spent another week in the shop, and, once again, the mechanics have been unable to find anything wrong. We have AAA, but I really don’t want to use the towing benefit any more than I already have. I think this easily qualifies as a “stump the chumps” question. They’ve checked the draw on the battery and various electrical components. The car has yet to die at the shop, so they can’t fully replicate what’s happening. Help!!! Any ideas, anyone?

Does this car have a key pad on the door?

No, it unlocks with the keyfob remote or with a key.