The Blankie Dilemma

Three of my daughters love their blankies. Interestingly, they are the same three who suck their thumbs. They need their blankies at bed time. They need their blankies when they're tired. They need their blankies when they are sad. One blankie, though, is on the verge of disintegrating. 
You think I'm joking? Tortilla has started this bad habit of chewing on her blankie. Not just nibbling a little corner but putting a huge chunk in her mouth and gnawing on it. 
Initially, we all treated it as a joke. "Ewwww... get this wet blankie off me!" No one wanted to be near Tortilla's blankie. Unfortunately, this bad habit is destroying her blankie. It's full of holes and it's becoming frayed. 
Yesterday, I pointed out to Tortilla how terrible her blankie looks. I gave it a hot, hot "bath," trimmed it the best I could and gave her strict instructions not to chew it. It was hard for her. She really wanted the blankie in her mouth. It's a cotton blanket, so I'm not sure I can mend it too much. Hubby suggested sewing a border on it, but because of the material I think a border will pull in the wash and ruin it more. For now, the frayed edges have been trimmed, but it's still a "holey" mess. Let's hope she values the blankie enough to give up the chewing habit or I'm afraid this blankie will soon be a goner.