Does this heater have a D2 power vent? It is an optional accessory to the heater (a fan). It "pulls" the exhaust out of the heater and of course it makes noise. So you can tell fairly easily if you have one or not. If you do have one, the air flow switch or the wiring to it is having an issue, or there is some sort of an obstruction like stated above, but that wouldn't necessarily explain the on again, off again operation.
If you don't have a D2, it gets tricky. The fact that it works for a while then quits tells me that it could be an expansion / contraction issue. Vent loop (orange wire) on board plug makes connection and satisfies vent switch loop when cool or cold, but when the heater has been operating for a while and heats up the board, connection is lost and wont re-fire. Maybe a broken trace on the board (worst case), or a wire partially eaten through vent loop on plug to board.
There is another diagnostic, if the display is alternating between FAN and TAb. But i wont bore you with that since you have been running ok in the past.
Either way, good luck.