Not familiar with that saw.
But it sounds like fuel related.
Is the carb adjustable, try screwing out the H screw a quarter turn,
screwing anticlockwise is out, this allows more fuel into the engine.
If there is a spark screen in the saw, is it clean or all blocked
up with soot, they need to be taken out and cleaned from time
to time depending on use, that may cure the problem.
Have you tried loosening the Fuel cap when this issue happens,
be careful, turn the saw on its side and remove the cap, that will
release any pressure or vacuum buildup and allow the carb to
draw fuel for the engine, if this works, then the tank vent is not working,
I have no idea where the tank vent is located on these saws, but stihl will know.
Are all the fuel lines good, is there a primer bulb on the saw, it is cracked,
there is also a vacuum pipe from the cylinder / crank case to the carb, is this
pipe cracked, split at the ends, or hanging off, is it or any of the fuel pipes spungy,
they go spungy over time due to the fuel softening them, they will then close
when suction is applied and starve the carb and engine of fuel.
When was the last time the carb has been serviced, the diaphrams and gaskets
go hard and need replaced from time to time, they do not last for ever, there is
also a metal gauze in the carb to collect dirt, it needs to be cleaned too.
If you can take off the muffler and look at the side of the piston
to see if there is any scores on it, if so then it may be too late
to save the saw.
If no scores are found on the piston of seen on the cylinder as
you look in the exhaust port, then its worth finding the fault.
If your then sure the carb is good, the fuel is good, the fuel lines filter and
vacuum line is good, and the tank vent is not the problem, then its time,to
look for leaks in the case, there are two seals one at each end of the crank,
and a joint between the cylinder bottom and the case,
they need to seal against pressure and vacuum, let the saw warm up, then
use some solvent like penetrating oil, spray it around the location of these bearings
and the case joint sides, if the saw sucks it in it will die, or change tune,
if this does not happen, then use some soapy water with a spray bottle and repeat,
spray around the bearings and the case joint and watch for bubbles,
there should be none, if there is then do not use the saw
until you find the cause of the leak.