2000 Pontiac Grand Prix Shutting off while driving

I have a 2000 Pontiac Grand Prix that keeps shutting off while driving. Been an on going problem. I cleaned the battery connections because they were bad but other then that i am kind of at a loss. It start right back up if you pop it in neutral and start it but tonight we had to crank it a few time and wait a few mins. After we got it started it died again within a mile but started back up right away while coasting and got us the 5 miles home. Kind of leaning towards a fuel problem. Was wondering what everyone thought and if anyone knows of any test to find out more. It just comes and goes.
Thanks