Keep them vertical and dry. That way they'll last for as long as you want. If you leave a paper background permanently up in your studio with a Manfrotto style background support, you'll notice a slight sag in the middle after a few months, particularly if you live in a humid environment. My solution is to source an appropriately light weight, yet strong aluminium tube; get one that is the correct diameter to fit snugly inside the cardboard tube/core of your paper roll. Cut it to length, just a touch longer than your paper roll.
With the Manfrotto style background support with the thingys that expand/grip inside the cardboard tube, then you need to do this. Get your angle grinder and make four 6-8 inch long cuts at each end of the aluminium tube. This allows the Manfrotto expanders to grip snugly on your paper roll. Without the cuts, your paper roll will just spin on the aluminium tube. There you go! A handy little home-grown invention.