1993 Honda Accord Most of the time it starts, sometimes it

Engine Performance problem
1993 Honda Accord 4 cyl Front Wheel Drive Automatic

Hi,
I have a '93 Honda Accord LX with a mystery problem. Our mechanic is baffled by this one.

Every so often, the car would refuse to start. The starter motor spins, but the engine won't catch. If we'd let it sit for a minute or two, then it started just fine. Our battery was old, so we thought that replacing it would solve the problem. Two weeks ago, on July 3rd, we replaced it. This seemed to solve the problem as the car then started every time.

Yesterday, we were about to leave a parking lot where our car had been parked for about two hours. It wouldn't start, just the starter spinning. Same problem as before we replaced the battery. We waited for one minute "” no good. We waited another two minutes but with no luck. Finally, we waited for a full five minutes and tried starting the car again. It started as if there was no problem.

Any suggestions? Thanks!