On very rare occasions I have a start problem that's been puzzling me and I wondered if anyone might be able to help. Symptom occurs when I start my car and move it several feet and then shut it off (as when I'm moving it out of the way for someone else). The car is probably run for less than a minute. The next time I attempt to start the car it is very difficult to start, cranks fine (not battery problem) but will take several tries and some very long crank times. It will eventually start sputtering until it finally catches and runs rough for about a minute, then it is all good again. Runs and drives fine afterwards. Happened just the other day and hasn't happened for more than a year before that (basically because I haven't needed to move it a short distance like that ever). The time between when it starts fine the first time and the next time when it doesn't start is usually at least 1/2 hour and as in the case the other day, as much as four hours have passed.
Anyone have any ideas what's going on here? Oh, and btw, I do not have any CEL.

Thanks for any help you can lend.