You may have a leaking seal. Does it die if you lay on the other side? This is called a roll out test, where you hold the saw, warmed up at idle, straight out in front of you. Then roll it over so the flywheel side is up, then back to normal, then roll it to the clutch side being up. The idle RPM should not change more than a couple hundred revs. If the seal is bad it is leaking air into the crankcase, leaning out the mixture, and can ruin the engine if used for very long. Older saws may have dried up, cracked seals. A pressure and vacuum test of the crankcase is how I check, using soapy water to look for bubbles if the crankcase will not hold steady at about 4-5 PSI under pressure.
And it may be a fuel line pick-up problem, as the previous post suggested, and that is easy to check, so do that first.