Acura Integra 5 Sp 95 starting problems after short stops

When I start my 5 speed 1995 acura integra after not using it for > 2-3 hours and then I drive it for a short while say < 10 minutes and when I restart within 5-10 minutes, It cranks but does not start. Then I have to not try cranking for 1-2 minutes and then after prolonged cranking it sputters and starts. This behavior is aggravated when it rains. There is no problems in the morning or after stopping and starting after long periods says 5-6 hours.

I took it to honda dealer (no acura dealer in my town) and he tried to reproduce this problem at least twice - leaving it for 2-4 hours and trying to start but he could not reproduce the problem. Initially he had suggested the relay but other symptoms did not fit that remedy.

Any suggestions.

The car has 130k miles. It was running fine till last august when I started having this problem.