A classic case of the main fuel pump relay is bad. Inside the relay module are 2 relays, a few diodes and a printed circuit board. The solder joints crack with age and temperature cycling. Quite common on 1990-1993 Accords.

http://techauto.tripod.com/

You can change out the relay yourself in about 30 minutes. Relay costs about $55 at the delearship, less if you can find it on line. EVERY Honda dealership knows all about this problem, but it is so easy to fix if you know the secret.