My 1996 Civic EX Coupe has had this problem suddenly show up the past couple weeks.
Symptoms:
-Occasionally will start (crank and turn over) then stall out within two seconds.
-Only stalls out on startup, never any other time.
-After the first failed start it usually will do the same crank and turn over but worse and worse each consecutive try until it just cranks.
-Usually will start normal again after a few minutes of rest and with a small amount of throttle after it turns over to convince it to stay running.

I've tried:
-Tested MAF Sensor, no issue also no rough idle
-Unplugged battery then reconnected and ran at 3k Rpm for a while to "re-teach the ECU where idle is (saw in another forum).

Other suspects:
-Idle air control valve (but only issue is on startup)
-Ignition switch (but no issue when wiggling key)
-Main relay
-Fuel Pump/pump relay (but no loss of power)
--Starter (but cranks and turns over)
-Fuel injectors (but runs fine once started)

Any advice is appreciated!!!


EDIT:
It's been three days and I haven't had the issue since I replaced the fuel filter. It was the only thing left I could think of that could keep my fuel flow low during start but still allow me to run. I tried everything else. If it comes back, I'll update here.

 

I had this happen once with similar symptoms. The rotor button inside the distributor had the screw back out which caused it to wiggle and not make good contact. Once the screw was installed everything was good to go. Also did you try holding the gas pedal partially down while starting to see if anything changes?