Fully warmed up Check Engine light does NOT come on

2005 Pontiac Sunfire: 15,000 miles - driven 3-4 times per week - usually short distances 2-10 miles - a little freeway driving. When I come to a stop, then press on the gas nothing happens (car remains at idle rpm of about 600). Or the car bucks forward a little.

Sometimes I can get the car running again by pumping the gas pedal. Rarely the car stalls. If the car does not stall, I generally have to turn off the car and restart the engine. Car then runs fine. The problem generally doesn't occur again for a couple months, but it has hesitated after stopping two of the last four times I've driven it. It only happens after coming to a stop.

Engine can be cold or fully warmed up. 'Check Engine ' light does NOT come on. I tried using high octane gas. That seemed to help for a while, but now the hesitation happens even when running 81 octane gas.