One of the issues with marker ribbons, especially those not made of satin, is that they fray, become unsightly and eventually fail to serve a purpose.
Well to help, I have discovered a product called Fray Stoppa (other similar brands are also available!). You place some of the clear solution on a piece of paper, dip the tips of your breviary or missal ribbons in it, allow to dry for no more then 5 minutes and hey presto no more fraying!
It is unobtrusive and for around a fiver, it will add years more service to your sacred books. I bought mine via Hobbycraft but it can be bought online from various outlets.
[I am now told that a viable alternate is clear nail varnish!]