Check your wiring for any after market splices. we had a car that had a problem similar to this except this splice was in the power to the starter wiring. some one before us had cut into the line, then just black electrical taped it back together. as the car heated up on the drive to wherever we went the wires built up heat/resistance and pushed themselves apart.

we would go out to see the ladies on friday end up at the spot and when we jumped in to leave sometimes/alot of times the car would not start till it had cooled for a while. this problem was the most perplexing and annoying. it stumped many a mechanic. most thought it was over heating but it was not.

it was just a shitty .12 cent back yard mechanic quick fix that drive people insane trying to find it.

So in the interest of not going insane, check all your wiring. look for cracks, after market splice ins. It sounds like a resistance problem to me.