When the car starts it runs fine as long as we don’t shut it off. The problem seems to be on repeated startups either hot or cold. We start the engine once, run it for a short time, shut it off and start it again a second time and once more we run it for a short time. On the third attempt to start it up it refuses to start. It seems to be always on the 3rd attempt at startup. If let it sit for some time–1/2 hour or more it starts again ok. Weird!
Mike
Try replacing the fuel pump relay under the dashboard. These relays are a common cause of difficult starting on older Hondas.