I'm having the same issue but mine will need two starts once the car has sat more than two hours, also the car has suddenly gone off (while driving) twice in the last one month and only started after I let the car cool for about an hour

 

inspect ignition switch. can be cleaned but better to replace:

DIY Ignition switch cleaning - Team Integra Forums - Team Integra

more fun links:

Starting Problems

Advanced Ignition Troubleshooting - Team Integra Forums - Team Integra

Honda Acura Essential Electrical Repair Website. Troubleshooting Main Relay, Coil, Igniter, etc.

 

Just wanted to say that this started happening to me immediately after I went turbo. 91 CRX HF, b16a. If I simply turn the key over, it will rev up a bit and then die (engine cold or semi-warm). I always start the car with my foot just barely touching the gas pedal for 2 seconds and it avoids it, then I can let off).

Few things that could cause this but they are mostly related to if you boost your car:

• vac leak on map sensor (most people T off this line to BOV). (this happened to me so thought I would mention)
• vac leak on FPR line - common to tee off this line to boost/vac gauge in car
  (cheaply made BOV's and or boost/vac gauges can leak and cause a vac leak on the line you're tee'ing to. If either of these lines leak, it can cause these problems)
• modification to the iacv or fitv on the intake manifold - if you plumb your coolant lines to turbo via these, you can affect your idle, and startup.

In case you're wondering, I'm still having this issue. I *think* it has to do with the way my coolant lines are plumbed via the FITV under throttle body. I'm still trying to pinpoint it. Hmm, it could be battery/ground related. I didn't relocate my battery to trunk like most who go turbo. Instead, I put in a motorcycle battery up front to make room for chargepipes. So now I'm wondering if it's battery/ground related.