1997 Mazda Miata

Problem started when the engine seemed to be misfiring. We replaced the plugs and plug wires and fuel filter. The car ran great for about 60 miles, then it stalled at a red light. After that the engine would crank but would go dead. After about 10 minutes, the car would crank and idle and seemed to be fine. About 2-3 miles down the road, it stalled again and had to be towed. I let it idle in the driveway for about 30 minutes and everything seemed to run okay, so I drove it about 3-4 miles with no problems. After that we accelerated in 2nd gear up to about 5500 RPMs and the engine stalled. The check engine light does not come on. The engine will start but immediately goes dead. After 5-10 minutes to cool off, we were able to drive it back home with no problems.

What problem does the car seem to have with this information?