l will drive the car and at various times, the engine just cuts off. There have been some instances when it is been on the highway and some local road. l am able to simply pull to the side of the road. When the engine cuts off, it is only the engine that conks out, the rest of the lighting and accessories are still on as they should be. When l pull to the side of the roadl have to wait anywhere from 5 minutes to 1 hour to be able to put in the key and restart it

my first thoughts r that the ignition coil is overheating & going open circuit so u lose the spark to the spark plugs. that is very common on the older honda cars.

i recommend u check for spark if u can when the car wo not restart. l realize that it takes two people to do that & u probably drive alone so it might not be a practical recommendation.

there r other possibilities such as an ignition switch & the ignition module but as a percent of total possibilities they r much less likely than a bad ignition coil.

sometimes the tachometer will bounce before the car cuts out. if that happens its a sure sign its the ignition coil.

ignition coils r relatively inexpensive. I'd certainly try that if l was unable to test for spark when it happened just based on the odds.

hope that helps

l had a similar problem when l just bought my CRX three years ago. In my case it was a dirty rotor and distributor cap, however follow first Honday guy advice, he helped me to find an oil leak that l wrongly thought was a burning oil.

l had a 1991 accord, Lx, 5 speed.It is a great car! There r two known issues with that car. the distributor is one ( l think there was a recall) & the main relay is the other. l am guessiing that it is the main relay. When the engine heats up, the main relay expands & looses it is connection. It basically disconnects ur alternator. thats why u have to turn it off & let it cool down before it will work again. Go have them check the main relay.
usually it acts up when the weather is hot. But it can happen whenever the engine gets warm.

l know u made a comment that all the lighitng & accessories still work but do ur dash cluster indicator lights come on when the engine dies or do they remain off? If they r off its will most likely be the ignition switch.As Honda Guy said the odds to be is that ur coil is shorting if ur lights come on when the engine dies(watch the tach). l think Honda Guy is leading u down the right path but certainly dont try a main relay(as this will mainly cause a no start during warmer weather after the car has sat outside with windows up). The main relay shuts off power to the fuel supply when it fails. Distibutors going bad will screech & squeal before they fail & when they do they lock up.GOOD LUCK!