I had a plymouth that did that. It turned out that there was a label in the gas tank that was floating around and would get sucked toward the fuel pump and it would shut down. After the car sat it would float away and it would run fine again for awhile. Not sure how a label would get in the tank seeing that I bought the car brand new and didn't get this figured out until after the 7 year/70,000 mile warranty. Not sure if this helps but it is one more weird thing that I have figured out the hard way owning cars.