Q: Electrical issue

I have a 06 Saturn vue that I started to have issues with the electrical the battery light turns on in the dash and then all kinds of lights turn on a little after. The car runs good until I turn on the ac. I know the ac pulls more juice so it forces the motor to kinda loose power but after the ac being on for awhile the car will loose all of its power and the lights On the dash will turn off. After that the car will turn off and it won't start. I try to start it and sounds like a dead battery. I jump start it and starts right up. The alternator is good according to autozone I took it in and had it tested by them. Any idea of why my battery keeps on draining? Thank you.
My car has an automatic transmission.