The E10 mixes break down much quicker than straight gas and the stabilizer helps prevent breakdown, but ethanol based fuels also absorb moisture which causes ignition and corrosion issues. Even if the the genset is purged of fuel at shutdown, the supply tank is still suspect.
The guys that let fuel sit in carburetor jets or fuel injectors for extended periods find many more blockage symptoms and it can look pretty nasty and sticky. I don't think this the cause of the OP's problems since he fires up the genset once a month to prevent fuel from sitting.