Your 2001 Accord was not part of the great ignition switch recall, but the ignition switches of all Honda vehicles in that era are suspect. If the warning lights do not come on when the car dies the switch is failing; if the warning lights come on as expected the problem is elsewhere.

First best answer to bmwrider001 - the symptoms, especially the 20 minute cooling off period, strongly implicate the igniter (aka ICM). His test is also about the only test you can do in the field, and getting this to fail when a mechanic can see it would be a stroke of the wildest luck. I am not in favor of throwing parts at a problem but the likelihood of this being the ICM and the difficulty of catching this in the act make it a good bet if the indications of a bad ignition switch are missing. I have never heard of a main relay causing an engine to die once running; the vibrations usually keep it alive until the engine has to be started again. In any case, you would be complaining of hard start or no start first.

Sounds like your Honda is under the control of SLENDER-MAN ! This is very dangerous. Leave the car running in a mall parking lot with the key in it. This is your only chance to save yourself! I'm serious--do it today! You'll thank me for it when the thief who steals it winds up dead.

The next time it quits on you, check for spark (pull off a plug wire, ground the shell of a test plug and attach the wire to it) If there is no spark, then after a cool off period it restarts, most likely you should replace the ICM or igniter -- a very common failure.

Sounds like the main relay could be starting to fail, about $50 from a parts store

I think your catalyst converter is bad/ dirty try buy a new one.

http://dmlawyer.com/car-accident-attorne...

I have a 2001 Honda Accord 4 cylinder with 195k miles and the problem that I'm having with her is that while I'm on the freeway or the streets my car shuts off and if I'm lucky it turns back on within 5 seconds as its moving, sometimes, and this is more often, my car shuts off that I have to pull over and stop my car completely and I take my keys off the ignition and put them back on to turn on the car but won't start, so I have to wait about 20 minutes to try to start it again and it finally turns on like if nothing happened, I feel like she's playing games with me, what could be the problem? I have no check engine light and I always maintenance her, my engine doesn't run rough, and I still feel she could take on another 100k miles by the way I take care of her but this easy fix problem that I'm having I would appreciate if someone gives me the BEST answer, idea, or even advise so I could figure out what I could do as quick as possible because I can't afford to lose my job over probably the easiest fix to do to my girl since she is the only bae I have to take me to work, Thanks Guys!