Ask Smithy Xtra Honda Accord start up problem

My 1988 Honda Accord Sedan 2.0 Si generally runs very well, but has a problem starting. It either starts immediately, or not at all. The engine turns over rapidly with the starting motor, but will not fire. A mechanic believed the problem was with the oxygen sensor and replaced it, but it?s still happening. The problem mainly occurs after a 15-minute drive, then stopping to shop. It will then fail to re-start. It does however start easily after sitting for the night.