The compressor is belt driven and stops with the engine when you shut it off, so I assume only the fan is running when you leave the a/c on. Is it running the battery down to the point that the car will not crank over with the starter? Or will the starter crank the engine, but the engine doesn't start?
The problem is when I live the A/C on and engine off for a while, if I try to start it, doesn't do anything, If I wait a while it does start without a problem.(10 to 15 min).