1989 Honda Accord 1989 Accord engine cuts out

The engine on my 1989 Accord cuts out, from time to time, while I'm driving. All of a sudden, the RPMs go down to zero, and the car coasts along. It happens on turns, on straightaways, even going downhill. It happens once or twice per tank of gas. Full tank, half-full, etc. I've used dry gas, gas from different vendors, and 89 and 91 octane. Also, it can sometimes be difficult to start up after it cuts out. The engine starts, revs up, but as soon as you take your foot off of the acclerator, the RPMs go back to zero, and that's all she wrote. Other times, it will start right up. The last time it cut out, I turned the key in the ignition, and gave it just enough gas to get to 2,000 RPM. I kept my foot steady on the acclerator, and was surprised to see the RPMs drop to 1,000, go back up to 2,000, drop to 1,000, etc. For about 15-20 seconds. When I took my foot of off the pedal, RPMs dropped back to zero. Eventually I was able to get the car moving (a quick shift into D) before the engine cut out, and was able to keep it moving. I got it out on the road and it ran fine. I've had the car to several mechanics, to include the local Honda dealer, and they haven't a clue as to what the problem is. Any advice would be appreciated!