Check with the manufacturer. This question comes up a lot, and there are strong opinions to both sides.
Personally mine are ok to leave down, but, last winter one froze to the ground when I was trying to leave for a trip. It was stuck and took a good bit to free it up. I don't leave them down especially since there is no real good reason for me to do so. If you are storing it why would you want them down? I've heard arguments about flat spots on tires but that's not really an issue anymore on newer tires. A tire doesn't care if it's in the air or has weight on it no more than your stored RV cares if it's level. They can dry rot just as easy in either case. Being on the ground or with weight does not accelerate the process. If you really want to protect your tires, take them off and store them in a garage, otherwise, elements are elements, weighted or not.
Unless your manufacturer has some reason to one way or another I really don't think it matters. But I never really did understand the logic of storing them down. What's the point? What benefit (documented) is there to taking weight off the tires?
One thing is certain, if you have an issue when you go to take it out, it's a whole lot easier if your issue happens when jacks are in the up position than down. You're stuck at that point.