yes, old gas is bad- ( we are looking at you, Iowa)- the ethanol which dilutes our gas causes deposits and introduces water into our fuel systems. ( that water can rust through a fuel tank)
it doesn't as much affect fuel injected vehicles, but anything with a carb can be a problem- small motors, old cars, motorcycles.
you could try running a chemical cleaner through the system and when stored stabil or other additive can help.
I have the onan and a petcock on the fuel line, this allows me to shot off teh gas supply and the genny will run almost all the gas out of the carb before stalling.
a local small engine shop may be able to suggest the best carb cleaner ...something they have had luck with on chainsaws, snow machines, landscaping or farm equipment
Mike