'93 won't re-start for a short while

We have a '93 Storm that has just recently given us problems when we try to hop back in the car to go out again. It has just over 100k mi and runs great otherwise. New coil 3 months ago and new wires, plugs, cap, etc + fuel filter less than a year ago.

It always starts in the morning and if it has not been driven for a bit, but if I have driven for 15 miles or more and stop, then try to re-start in 5-15 minutes it will crank but not fire. The 1st time it happened, I found someone to show this to and by golly- it started! The 2nd time I waited about 15 minutes, got frustrated and just took a different car(not usually available). I tried it much later and it was fine.

Personally- I am thinking vacuum of some kind.