Its been quite a few years since we had our PW but I remember having some sporatic problems with it. What seemed to cure them was:
1. Disconected the oil pump and just ran premix
2. Look for water/moisture. Take off the ignition cover, pull any connectors apart and blow them out gently with compressed air. Let it sit there opened up for a few minutes. I also used liquid electrical tape over most connectors.
3. Take off the carb and thouroughly clean it.
4. Remove the pipe and clean it out. The best way to do this is to throw it on a fire or use a torch but be careful because you will get flames coming out of both ends. As the pipe cools tap it with a screwdriver to loosen the burnt carbon and shake it out.
I'm sure there was more including doing the top end, but that should get you started. Hope it helps.