I had a similar problem for a couple of years,
finally dug into it when it stopped entirely.
Turned out to be the fuel pump.
They have 2 valves inside, and they are retained in place by a staking operation in the housing.
It failed after many years operation, so one of the valves was flopping around instead of remaining in place, thus it didn't pump when the valve was out of place.
I was glad it happened though, as the diaphragm was badly worn/frayed and in a short time would of ruptured and filled the crankcase with fuel, which could of caused catastrophic engine failure.