I wonder if there is a short in the circuit board of the ECM. When it gets hot it could randomly short out, then after you sit for an hour it cools down, the circuit closes back up and then it starts again. The fact that it randomly stops could be vibration at just the right time when it is heated up.
Do you know of someone with another similar model you could switch out with for testing purposes and rule that issue out?
I have a 2002, the only electrical issue ever was the ABS module stuck killing the battery, was looking for a replacement on E-bay and found some guys in TN that rebuild them and shipped it to them for a rebuild with lifetime warranty for under 40 bucks, that was back in 2010 and it still works fine today.
I also had the pinion bearings in the rear axle go out as well, I pulled a heavy travel trailer at 500 miles for a 700 mile round trip, it started making noise at just under 36000 miles and was covered under warranty.