...I took it right to the dealer and am still waiting to hear back...
I hope your dealer is good, and actually troubleshoots the saw, instead of just wading in and acting like a "Parts Replacer". Please let us know what he finds out.
In My Opinion, even though we've never met or talked, mweba is one of the 'smart guys', especially when it comes to the 555/562. I wanted to first think "air leak", but the lack of reliable fuel delivery (for whatever reason) makes more sense, upon further reflection, considering the description of the problem.