There is a relief relay that is designed to shut off power while the motor is cranking, that would be my first guess. I think it's a standard relay, but if you've tested the whole set it might be a little deeper.
I've also noted an under-voltage relay. I think it's near the steering column on e30's. It'll shut down the whole car to protect the electronics from low voltage damage. In that case it might just be the battery...