Yes fuel can go bad...have no idea how long it takes but I would say if it has been sitting for MONTHS (Years) there is a good chance it is not "as good" as it was/could be.
(Not to mention it coats the lines with a hard, "shlack" type substance...you see carb cleaners and fuel injector cleaners out there to help with this.)
I am not sure who said this before, but they had a gallon of gas in a bucket in their shop, and after the fumes all vented off, they literally would put out their cigeratte butts in it. (Yeah...who is the first guy to try, eh?)
Sam