What's wrong with my car part 2 (probably not the alternator)

Hey guys. Here's a follow up to "what's wrong with my car" In the first post everyone said it was my alternator. But if my alternator went out shouldn't that mean the car would have problems every time I start? I drove it around the block a couple of times on Thursday and hit 50 a couple of time(didn't want to test it on the high way) and it worked fine. And then today on the way back from the gym it died on me again. I kept cranking it back up every time it died until I got home. What I noticed was if I gave it enough gas to keep the dial above 1000rpms per minute at all times the car would run fine, but as soon as I let go of the gas pedal the gauge would drop and the car would die. Does this still sound like an alternator or is there something wrong with my fuel line? I had the pump checked about 3 month ago and the fuel filter replaced at the same time. What do you guys think?