Chainsaw Repair

About 6 months ago I got a second hand 3 year old MS181 C and the first few times I tried it it seemed to run ok. It then started to exhibit the following problem. At first I set the control lever to its lowest position and pull it over until it burps, then lift it one notch pull it again and it starts and runs well at a fast idle speed and it will continue to run in this condition with no problems. Once warmed up I gently squeeze the throttle and the lever lifts up another notch and the saw goes into its regular idle speed, but after a few seconds it gets slower and slower until it cuts out. If I try to rev it up it won't and sounds like its bogging down and then cuts out. I can then only restart it a couple times more before it won't start again until it has fully cooled down and each time it cuts out very soon. So far I have fitted a new air filter, cleaned the carb and fitted new gaskets and diaphragm, cleaned the tank breather and checked the fuel filter is not blocked and owing to a high resistance reading on the primary coil have fitted a new ignition coil. The spark plug seems to spark well so have not changed it yet, maybe I should. I have also altered the High / Low and idle settings according to the manual.
The saw still has exactly the same fault every time I try it.
Running out of ideas with this now, can anyone help please.

If nothing suspicious is found pulling the muffler, looking at the muffler screen, the piston walls, rings, and cylinder walls, the seals are very easy to replace if you remove the engine unit and take off the bottom pan.

someone may have already removed the screen? I don't live in an area that requires a screen and that's the first thing I take off the saw.

Yep my guess would have been the spark arrestor but if there is none then I would change out the fuel filter even though you think it is ok.   I have been faked out by the fuel filter before.    Also one other thing you could do is loosen the fuel cap to see if it stays running because of the tank vent.   

You're located in England and the mufflers do not have spark arresters there