1991 Geo Prism will not re-start after being driven

I have a 1991 Geo Prism, automatic transmission, with about 100,000 miles on it.

I typically use the car for an 18 mile commute each day, with the car sitting for many hours between each use. During this pattern of use I never experience a problem starting the car.

However, If I would make a stop after driving the car for a little while, even a 10-15 minute drive sometimes, the car will not restart. When you turn the key you hear a 'click' sound, but nothing else. The starter does nothing, as if the car has lost its power. I should add that if the car is restarted very quickly after it is shut off it will usually restart without a problem. But if I drive it, shut it off, leave it for a few minutes, then attempt start it will not go.

After the car sits for anywhere between 10-45 minutes it usually will usually start just fine.

Repeating these results for a mechanic has been difficult. My mechanic actually let the car run for an hour and then shut it off, let it sit, and then attempt to start it in order to get these results. However, the car has started every time for him.

Your thoughts are much appreciated.