GE Dishwasher - No Water Mid Cycle

We have a GE Dishwasher that is approx. 3 years old and it has started making a loud whining noise about two hours into the wash cycle. It sounded like a pump running dry and I confirmed that there was no water in the sump when the noise was occurring so I ran each pump in diagnostic mode without water and the noise sounds like it’s the circulation pump. When the machine makes the noise, if I open the door and dump 2 liters of tap water into the sump it will go back to running normally and ultimately complete the wash successfully.

I replaced the inlet valve and the machine ran two or three full loads without issue but the problem quickly returned. Every part works correctly when running through diagnostics and the machine runs flawlessly for the first 2 hours every time. Any help on where to turn next would be greatly appreciated.

After more experimenting, it appears that the dishwasher will not fill when it is [COLOR=Red]hot[/COLOR]. The unit will run through a full wash cycle but when it gets to the rinse stage, it will not fill with water. At that point, if i cancel the cycle and start a new cycle, it will not fill. If I enter diagnostic mode at that time and test the water inlet, it will not fill. What would cause this apparently heat-sensitive failure?