Premium gas is only advisable if your generator is running hot due to high compression, timing problems or excess carbon build up.
Using premium gasoline in your generator will most likely result in the premature build up of carbon deposits and actually make it harder to start. Premium means higher octane. An anti-knock / pre-igniion prevention measure.
Try to use Regular Ethanol free gasoline in your generators if possible and forgo the Premium.
Until you add Stabil Marine 360 Blue to the gasoline (not Stabil Red), you will continue to have problems from storage.
Stabil Marine 360 has a unique additive that coats and protects the surfaces of fuel related components and it is superb.
It is widely used by marine mechanics and boat owners for a good reason.
It stops oxidant related damage from moisture in it's tracks.
Obviously, the carburetor and fuel system must be in good working order before you add it.
You may get a lot of comments saying otherwise, but they probably do not have 50 years of engine building experience and the extensive background in motorcycle maintenance I have.
You can take this advice to the bank.
Get it. Use it.