I think storing it on nice big coffee cans or extension cord holders is the best idea to minimize coils but I just leave mine on the reels like Normand and always have with no issues.

I fish 12 months a year but the 2-3 weights and even some of the 4 weights definitely don't get much use during the winter. Those reels and their lines sit for a few months and reappear in the spring just fine.

Your mileage may vary...