Similar symptoms with one of my saws recently. It would starve from fuel periodically and it was a bastard to get started again. Turned out there was some slimy stuff of unknown makeup on the pump diaphragm keeping the little flappers from doing there thing.Initially, it started and ran fine. Idled fine. Then when I put it to wood and start the cut, it would stall and start to die after a couple of seconds.
To recap what I've done:
I replaced the fuel filter, but not the line. Ordering one now. I've replaced the gas tank vent and the spark plug (needed a new one). I've kind of inspected the impulse line and it looks OK. I'm going to completely remove it and inspect it.
Thought I'd check the easy stuff before tearing into the carb.