It's natural for a small child to develop a close attachment to a special, cuddly object - even when it's worn and ugly. Don't take it away or substitute a newer, cleaner version (although it's wise to get a duplicate in case the original gets lost). Security blankets are often a substitute for thumb sucking, and generally prove easier to give up.
If this precious object is accidentally left behind, say on holiday, explain that a holiday is a special time and that the blanket will be waiting when you return. Find a substitute to give some comfort: make a puppet out of a clean sock, or give your child something which smells comfortingly of you
