I have that problem with my 92 Accord, sometimes. It only happens after I have been driving it, (meaning it is warmed up), and I shut it off and try to start it again fairly soon, such as when I stop for gas. Mine lasts a couple minutes and I think it is coil or igniter related, let me tell you why I think that. And actually I think there is something temp sensor related going on also which I will explain in the following looooong explanation.
When I first got the Accord the bearings in the distributor were shot, screeching like crazy. I bought a rebuilt distributor from Advance Auto Parts and put it in. That was end of Oct. 2000. My first indication of any trouble was that winter. I left my house for work one morning got about 2 miles away, on the highway at about 60 mph, and it just quit. No sputter no nothing, just quit. I tried to restart while I coasted but no luck. I coasted about half a mile into a parking lot and stopped about to call my wife decided to try again... it fired right up and I continued on to work, 32 miles away, with no further problems. This happened once more that winter, EXACTLY the same way. It quit within feet of where it had quit before.
It didn't do it anymore through the Spring and Summer of 2001. The igniter in the distributor went out March 21 of 2001. No warning, I went out to go somewhere and it wouldn't start. Advance replaced the distributor, I love lifetime warranty, and I had no problems through spring summer and fall.
Then cold weather hit. It did exactly the same as it had done the previous winter, once again within feet of where it quit before. It did it every morning that it was cold enough. If it was 45 degrees out it wouldn't do it. It would only do it once a day and be fine the rest of the day. It gradually quit sooner and took longer before it would restart and did it with a little warmer outside temps.
I took it in to the Honda dealer and they said it was a bad coil and that they generally replace the igniter too. I should have just gotten another distributor from Advance but I decided I would let the warranty work fall to Honda instead. That did fix it but now I am beginning to have the problem you are describing.
When I had originally replaced the distributor I had noticed a blackening in the distributor connector, as if there had been some arcing. When it started quiting on me every morning I thought it had to have something to do with signals being sent to the computer as the car warmed up, since it would quit at the same place. I looked at the coolant temp sensor connector and the coolant temp sending unit connector. They both had the same blackening in the connector. I still think it is related and that something is sending to much voltage and killing my igniter and or coil.
It is almost Spring so I expect I won't be having any trouble for awhile but I sure hope I do before the 12 mo. 12,000 mile Honda O.E.M. parts warranty runs out.
Hope this somehow helps.
Michael