The problems you are having just don't seem right! Especially after having both generators "professionally" repaired. Did you take them to a certified Honda shop for repair?
I use a fuel stabilizer in my generator's gas tank since the gas sits for long periods (sometimes for months) between uses.
One thing I do religiously is start and run the generator under load at least once a month between actual usage.
The oil that I use in all my 4 cycle tools and the generator is an Amsoil synthetic product (note the temperature ranges). See here:
http://www.amsoil.com/storefront/ase.aspx
The synthetic is slipperier, has an affinity for metal (doesn't completely run off between uses), and has a greater resistance to heat breakdown than conventional oils.
Since generators and other garden tools are air cooled, the need to find an oil that stands up to the higher heat is very important.
