I agree with the above posts. It sounds like a fuel delivery issue. If it's just quitting, it could be either it's too rich and bogging out (biggest cause would be a clogged air filter- so clean it!), or more likely not getting enough fuel and just dying out.
If you have access to a compression gauge, do a check to be sure that the saw isn't in need of a piston or piston/cylinder.
You did the fuel filter, the next thing to check and replace as neccesary would be the fuel line and then the impulse line. If those are good, move on to the carb. If it is in any way dirty inside or the diaphragm is dried up that could be your problem. Take the carb apart and give it a good cleaning. Use gas or carb cleaner and blow out all passageways in the carb with compressed air. If you're taking it apart anyway, you could just rebuild it and be done. A complete kit for one only cost $6.00 here, so for the price you may as well.
Adjust it in (I believe 1 turn open from lightly seated on both the high and low needles should get you close) and then you can dial it in once it's running.
Hope this helps.