Storing rubber back rugs in the closet will make the back deteriorate. How do you store them?
I have used the air tight storage bags that you can suck the air out of with the vacuum cleaner for smaller rugs - but I did not leave them but a couple of months as they were folded and that is not good for rugs being stored a long time.
I believe cleaners recommend rolling them with tuff on inside and a layer of a cotton sheet as you roll - the rug can then be wrapped in another sheet and stored in a dark cool, dry area.
Heat is what makes them deteriorate. Store in a cool place. Don't put them in the dryer, either.
Heat is what makes them break down. Do you have a cooler place to store them?