I'd consider the possibility of contamination in the fuel tank that could be clogging the screen on the fuel intake line. I'd rinse/flush it out with some unmixed gas.

JM$.02W

Does it have a spark arrestor in the muffler? My Stihl has one, a very fine steel screen. It clogs up with carbon and restricts exhaust flow, which restricts air flow, which makes the engine act up. I'm not sure I like this as an answer though, if it's clogged up with carbon it should act up all the time till you clean it, not only when it's halfway through a tank.