Fuel injectors maybe?
 

This started a while back but was minor. When I press the gas nothing would happen but the engine would still be running. It would only happen for a second or two then the car would engage and go on it's way. I put some fuel injector cleaner in after that and it was fine for about a month. Now today it started again but for more prolonged periods of time. Enough that it is now very worrisome. The car doesn't actually stall it just doesn't respond when I press the accelerator...or it would respond if I were slightly pressing it but anything more than that and I get nothing. Any ideas here? This makes driving very unpleasant.:confused:

It's a 92 accord.

Sounds to me like you may be due for a throttle cleaning. Google "41yFXjibtLY" for a video on how its done.

Ccleaning the IACV, throttle plate, and throttle bore may help, however these items affect idle stability, and may not have much impact on acceleration.

The throttle position sensor (TPS) might have a "flat" spot that fails to communicate continuous throttle plate position changes to ECU. A gross fault would be detected by ECU, however a minor fault might not be detected.

Only way to know is to test the TPS output signal and look for a smooth change in voltage as the throttle plate is moved. There are testing procedures in shop manuals. If you don't have a shop manual, suggest a download of a manual from Online Manuals links in DIY forum.

The TPS is not available as a component, and you may need to purchase a used throttle body to get the TPS. Car-part.com can help locate.

good luck