1989 Honda Civic Wagovan

Problem began about two years ago. Sometimes the car would not start if
you tried to start it within a few minutes after it had been driven and
turned off. It would grind and grind. But, if you waited about 5
minutes, it started. Initially, this difficulty would occur rarely,
then more often. It always started if the car had been sitting a long
time, anywhere from 10 minutes to overnight, or several days.

About 6 months ago, though, it would not start at all. Luckily, this
happened one morning while it was still in the garage. No intermittent
problem this time - grind and grind, but no starting. So, we had a
mechanic test the main relay, all the electrical connections, and all
the fuel connections. He sprayed something in the fuel injector
mechanism, and the car started and ran - so he knew everything past
that was OK. He said we should hear the fuel pump run for a few seconds
when the ignition is turned to ON. But, we heard nothing. To be sure,
though, he circumvented the main relay, but still no fuel pump noise.
So, we replaced the fuel pump and the fuel filter. After he removed the
old fuel pump, he wired it directly to the battery, and of course it
ran. He said that kind of thing can happen. Well, OK.

After the replacement was made, the car started. And I turned it off
and started it several times, including after driving it for a while.
And it kept starting and running fine - for two months. Then, one day
after I had been driving for a while, I had to start the car after it
had been parked for just a few minutes. Grind, grind, grind, but no
starting. Waited a few more minutes, and it started. Same thing
happened a month later. I replaced the spark plugs, which had been a
bit overdue. Now we're having the same problem with the engine
grinding, but not turning over, if the car has only been sitting a few
minutes after being driven and turned off. I always listen first to
hear the fuel pump run, and it is running - every time, whether the
engine starts or not. One other thing to mention - our driving habits
with this car: it is mainly used for very short trips in our
neighborhood - no more than a few miles at a time, sometimes with
several consecutive short trips on Saturday mornings when my wife goes
to garage sales.

What do you think the problem is?