What is the problem keeping my car from shutting down after it runs for a while

What is your question?

I have a 1997 Buick skylark and I'm having problems figuring out why do my car shuts down after it runs for a while..it's not the alternator I got it tested twice..then when my car shuts down I get a boost off with the booster cables it crank right up then when I take the cables off the car shut down and go dead again it's something not keeping my battery charged do u have any clue whats the problem