Like Pat said, get those suckers dry, dry, dry before storing them away. I stretch them for several days until they feel dry. Then I trim the edges and hang them up in my shop for several more days. I wait until there has been several days without rain and then I roll them up and put them in a plastic organizer storage box like what you can get for fishing lures. I keep that box and any other animal parts in a large tote with borax lining the bottom. The borax is supposed to keep mites and bugs away.
Be careful using rubber bands to hold the skins in a roll. They can deteriorate over time and melt to the skin. I like to use twist ties.