@drgeoff - I did read that posting earlier and I don't doubt it might be a micro-crack on the board that expands just enough with just a little heat. My supplier is RS-Components, unfortunately they are on the other side of the ocean from me, so shipping is expensive and time consuming.
@malakai - I tried a USB charger for a DroidX, Evo4G and a Droid Incredible. I also tried with a Car changer for a DroidX. I also tried with just the USB cord from multiple computers. All the charger are rate for 5V. When I measured across TP1 and TP2, with the different chargers, it would read between 4.6V - 5V. Most of my testing has been with the DroidX changer. With RCA video, Ethernet, and Keyboard plugged in, the voltage hovers at 4.72V - 4.78V during the boot up. When it dies, it goes up to 5.0V. So, the voltage is on the lower end, but it doesn't explain why it works longer on a block off ice or why it needs to 'cool' down before getting it to boot again. I do have a Adafruit charger on its way which might help.
@redhawk - I tried figuring out 'where' it is overheating, but nothing really feels all that warm. While the Pi is booting and at the login prompt, the F3 polyfuse has between .19V - .21V across it. When the Pi stops working, it drops to .07V and stays steady. Does that mean anything to you?