When you get into the car, turn the key to on position but do not start the car. While everything is quite, do you hear whirling sound. If you do, that's your fuel pump creating fuel pressure. If you do not hear the pump making the noise, then as up_the_irons pointed out, it could be the relay (@up, is that what you meant by "main relay" or do those civic's have something else?).
Another possible cause is leaky injectors. I had an 89 acura integra (i.e. rebadged honda) and it had both bad relay and bad injectors. Relay was easy to identify. Injectors took me a little while.
But symptoms were kinda what you describe. If the car sits overnight, it would start fine. If I just drove it, it would start fine. But if I left it sitting for few hours it was very hard to start it. Explanation I eventually came across was that injectors leak while engine is off because fuel lines are still pressurized. If you just drove, they haven't leaked enough to flood cylinders. If the car sits for a long time, the gas will drip out past the compression rings into your oil. But at just the right time interval, you end up with flooded cylinders and a car that's really hard to start.
I went to a junk yard, bought another set of injectors, shipped them out to be professionally cleaned/calibrated, then swapped them in and never had tough start problem ever again.