I do keep mine in a box, it's a special acid free cardboard container. I can't use all of my quilts at one time and after using on beds and displaying many I still have more to store. Theses boxes are great for that purpose, they are stored in my clothes closet where I can get at the quilts and refold or get them out for use.
These boxes are made for the purpose of storing fabrics, quilts, clothing and such.