Got an interesting problem that I'm finally willing to try and solve.
We've got a 4+ year old propane water heater (came new in our new house), and ever since we've had it, it occasionally gets into a state where you'll use some hot water, and the exhaust fan will kick on, but the burner won't fire. The exhaust fan will then fun forever, as it seems to think the burner is on and needs to run. I go down and flip the on/off switch, and it fires right back up in the correct state. If you peek in the fire hole when it is in the confused state, there is flame in there - I'd describe it as more than a pilot light amount of flame, but far less than full blast when it is working right. Maybe the difference between your simmer burner and your rocket burner on your gas stove.
Back when we first moved in, it seemed like 3 or 4 times a year it would get cranky like this, and do this make 3-4 times over the course of a week or so, then it would go away and work fine.
Slowly over time, the frequency has increased, and the length of the time before it seems to resolve itself has increased as well. Seems to not have anything to do with weather, seasons, load on the the water heater, etc. Probably just a failing bit of electronics.
Anyway, before I have someone out, I'm hoping to see if anyone might have any idea if this is minor or major.
P.S. Might be meaningful: I've never drained the whole thing, but a couple times a year I drain a few gallons, and they're always crystal clear.