You can have a unit repaired, but the cost usually turns out to be almost as expensive as buying a whole new piece. Like Hersute says, it's usually just easier to buy a new one.

If you're having shedding issues in a particular area, sometimes it's because you scratch that area due to itching. I've noticed when I scratch any area of my lace, those areas always shed faster. Try not to scratch, and sleeping on a satin pillowcase really does help to keep the sides and back from shedding so much too.