even with Stabil, one year old fuel is probably your problem.
I would second this thought. Old fuel is not good anywhere and it leads to varnishing the parts in which it comes into contact.
If you are going to put the machine to bed for the winter it would be wise to do so with an empty a tank as possible. Which brings to mind the question what sort of procedure is required to restart the system once it has been starved of fuel?
