Why does my 1996 Chev. Cavalier sporadically sputter and die when I start it after driving a while, then shutting it off several minutes?

This is an intermittent, but not infrequent problem. I drive several minutes and then have it shut off, like when I go grocery shopping, but usually not when I just shut it off to run in a store real quick. If I can get it to keep going, it still sputters for several minutes while running, especially under load. It feels like it isn't getting gas, but then when the revs get up enough, it takes off just fine, though sometimes still cutting out a bit? Ideas? Suggestions?

2016-06-12T14:57:46Z

This problem has developed, and worsened, over time.

2016-06-12T15:03:05Z

I thought it was a clogged fuel filter, so I replaced it. The old filter was pretty clogged, and I thought that would fix the problem, but it turns out it's just as bad, maybe worse, than before.

KJ2016-06-12T14:59:14Z

I would say take it to the Chevrolet dealership and see if they know whats wrong with it. have you been charging your car battery? my dad has a 1969 Chevrolet Camaro SS and he always charges the battery when it is in the garage. try charging it and see if that helps. is it a manual? are you not shifting gears in time? is it a automatic?