I had the same problem in my Alaskan camper with my Fantastic fans. I did like above except with a tiny bungee cord, never had a problem again
FWC factory made some little bungees for me the first time - all that did was cause the handle to strip out against the still rotating "shaft" inside. So instead of stripping out more of those plastic handles, I took mine off completely and ziptied the lid to the fan blades - evidently I didn't zip tie it tight enough because it was able to force itself up enough to break the plastic tab on the inside of the cover! I'm going to a maxxair - the one arm lift design isn't so great in my opinion.