Samething happen to me. You need to buy a new ignition switch from GM with a new key with pellet. I bet you anything its that. What I did to mickey mouse it for the meantime was measure the resistance of the pellet on your key and buy a radio shack resister and just plug that in into the VATS module underneath the car. It work for many months that way until the little resister would fall and I would have to get underneath the car and plug it back on. Truly a hassle, so just fork out the cash for a new ignition cylinder and key and have someone install it and presto, problem solved. I also taught it was a heat soak condition because I had exactly the same symptoms as you just described. Even bought a new mini-starter for it. The car would not want to crank over nothing, like if it was totally dead. Then I would come back to it in a half hour and the car would just start.
What happens it the thin wire wears out and cause excessive resistance that doesnt allow the vats module to send the signal to the starter. Your other option would be to bypass it. Just do a search here or at Thirdgen.org
Let me know if this cures your problem or not.
of course thats just a guess 
