Hello Jay,
How about sediment in the fuel tank? Top off the fuel and see if it helps. If the entrance to the flower pot, in the tank, becomes clogged with sediment, the engine will starve for fuel after a short time. If let to rest, it will start and run again for a while. Topping the fuel level allows the fuel to run over the top rim of the "flower pot" and will allow the engine to run without fuel starvation.
Not much chance that the WRD is the culprit. Check it by seeing if its air intake is open during cold running and closes after warm up.