We had the same problem with our Fantastic Fans. The company said it was a problem with the adhesive they used to secure the rubber gaskets and caused to rubber to get sticky.
They sent out new rubber and a tube of adhesive to fix both our fans. We were instructed to remove the old rubber, clean the rim around the fan with rubbing alcohol, apply the adhesive to the inside of the new gasket and then attach to the rim of the fan.
It worked GREAT!! Now that's what I call customer service and we're happy campers over this fix.