I don't think you need to let it run 24/7 while in storage.
If you have a vent cover, the open lid has allowed enough air to circulate for my trailers. Having a covered second non powered vent is very helpful to exchange air.
The other thing that happened to me was having the fan motor burn out.
It was explained to me by having everything closed up tight with the vent fan running. It caused the fan motor to labor and i think that caused the motor to burn out prematurely .
How i was taught to test it was too have everything closed up tight except the Fantastic fan vent.
Now with the fan on , open the entrance door and you can hear the fan increase its speed to normal speed.
If you hear the motor speed increase, things are too tightly sealed in the trailer. Opening that second non powered vent did the trick.
P.S. air is allowed to be pulled in through the furnace vent on some model furnaces but it was not enough air to allow the fantastic to operate in full 'zoom mode' . More air flow, like a second covered roof vent was needed .