Yes, your generator needs to be run periodically or it will not be happy. Every month you should run the generator for two hours. There should be a load on the generator, which can be the roof air conditioner in the summer or the Truma heating system in the winter. (NOTE: It is okay to run the generator when you are driving.)
Or, as TOWB Admin Scott Baldassari said:
“Run it when driving,
Run it while parked,
Run it in sunshine,
Run it while dark.
Run it whenever
It doesn’t really care,
Just make sure you run it,
. . . or pay for repair.”