OK.....so I was able to save the fire last night and I finally went to bed around midnight.
The ash had built up to the point that it choked the fire, even though I shook the grates at least several times per day and aggressively enough that hot coals fall into the ash pan. After each shake, I empty the ash pan outside and so the pan is always clean.
With this mild weather, the PEA just simmers along, not turning into a fine ash, but remaining nearly whole chunks which doesn't shake out unless I turn the grate to about 135-150 degrees which must be close to dumping the fire. Just rocking the two grates on this Hitzer is not enough, they are too wide and flat, most likely a compromised design for a duel-fuel stove like this one.
Edit: The evidence that convinced me that the fire was choked of air was when I had a fan blowing into the ash door and the fire not even flaring up from all of that high-velocity air.