You might be able to solve this problem by asking a dermatologist for a prescription for Efudex. This drug is intended to reverse pre-cancerous changes in skin. If you use it very lightly on your lips (the dermatologist might be horrified by the suggestion that you do this) you can "sand" your lips, basically taking off the damaged surface and breaking the cycle of peeling/regrowing the lip tissue. In a couple days your lips will be covered with clear plasma-filled blisters. These will be protecting the new, healthy tissue. Your lips should be completely healed in a week, and you should not have to repeat this process for several years.
You can also try protecting your lips with duct tape at night. Apply mentholatum and then tape half-inch wide, three-inch-long strips of duct tape over them, fastening the ends to the skin.
duct tape on my lips? hahaha what?