Car will not stay running.

What is your question?

I have put in a new battery and had autozone test the alternator. Per them it is charging correctly. But as I'm driving down the road. I lose all my electrical. The radio goes out, the heater goes out and gages go dead. The car stills runs but only for a couple of minutes. then the car stops running. I have to hook up jumpercables to get the car started. It will run for a little while but then do the same thing over and over again. WHY???