1990 Honda Civic Lx,- car dies in drive, in park on heating up

1990 Honda Civic Lx, 1.5 ltr- (The relay switch was replaced just one year ago.) - drove the car about 3 miles-warmed up to the usual engine temperature (summer/SF bay area-mid am, not too hot outside yet). The engine faltered and then died in less than 10 seconds without any sounds from the engine. Check engine light came on. Waited about a minute and it started up-no problems. I drove to the local hardware store (bought some water for the car just in case) -checked the water, oil, battery connections. Put about another 15 miles on the car without this problem and parked it for three days. Started it today, same problem after driving about 2 miles but no check engine light this time. Parked it -came back 45 minutes later. Decided to start it and let it idle in park to see what it would do-engine died the same as before (on heating up to its average driving temp.) It started up right away again, drove it 1/2 block, and the engine died just as before.

Is this a common problem? Any ideas?

Thanks, Ann