Im seeing wiring fault if its not vacuum related. Likely have a short.

I had a reverse light switch that would ground to the tranny every time I put it in reverse and the car would die.

Also check your battery level when it dies..seems unlikely since it starts back up, but its worth looking. if the alternator for some reason isnt providing a decent charge the battery will slowly drain (slipping belt, bad alt etc) and youll see things like the stereo and tach dying when you apply the brakes..but again the battery would be almost too dead to restart the car.