For years I've used nothing but rubber bands to keep rolls from coming
loose.  There are things to consider.

First is to use rubber bands that are not too tight.  Second is to
treat rolls that are to be stored slightly differently.  In this case
I wrap a page of blank paper around the music roll then put the rubber
band around this so if it decides to disintegrate it will affect only
the clear page of paper used to wrap around the music roll.  Third is
to use rubber bands that have some width to them and make sure they lie
flat around the paper.

With several thousand music rolls it pays to learn a good system of
taking care of them.  Whatever works to your satisfaction.

Hal Davis