I run my generator during the winter time also. I may not get it done every month it might be 1.5 months. Mine is diesel but I know the main reason for running is to get heat into the generator coils and dry them out.
On my small engines (and not all Hondas) I get my fuel from a place that sells pure gas without ethanol. We have a couple that sell gas this way. Then I add Stabil to the gas can and then add the fuel into it. I also have added fuel shut offs to my lawn tractor and my snow blower. I shut the fuel off and run them out even with the Stabil in the gas. I take the cover off my Honda and drain the carb as I had a problem with it once already. I also had trouble with my snow blower before the gas shutoff was added.
This is just to try and keep from having problems when I need to use them and can't get them to start.