I have a fairly similar issue and I'm wondering if it would be the same cause. When we purchased our house we were told this unit worked. We used it twice and noticed it turned off/on constantly. However it would stay on longer periods as it ran longer. basically at first cycling on/off every minute or two and gradually it stayed on for 4-5 minutes, then 10+ minutes until it just remained on. Also of note was that I had to hold down on the pilot for longer than the instructed 30 seconds (more like 2 minutes) to get it actually started the first couple times. When pressing the pilot knob down, there is a much larger flame and I assume this is where/when it generated the millivolts.
After the first two uses, it completly stopped working, or at least turning on. The pilot lights perfectly fine, and remains on. However no matter how long I hold the pilot switch down (instructions say 30 seconds), the main burners never ignite for more than 30 seconds and then shut down.
So, is the powerpile utilized after the initial lighting of the burners? Or am I looking at something else.
My hurdle now is when I installed the new pump, I disconnected the heater all together as I felt it was not working, so why bother. To test anything I guess I'll have to re-plumb the heater.