Check your hoses. The hose in the tank may be soft and collapsing. Check the impulse hose if it has one; that is what makes the diaphragm pump gas(goes from carb to crankcase). Check the tank vent too.
As long as you are at it, check the muffler for obstruction(is the spark arrestor screen clean?)
Are you using good fresh gas with a quality oil? I run my saws on premium, with Husky or Stihl premium oil. Fresh premium gas and oil...
The other possibility is the ignition is failing when it gets hot.
With todays gas, if I replace a filer, I replace the fuel hose too.
You might ask or search the chainsaw forum at arboristsite too.