When someone does something incorrigibly, they keep doing it, and nobody can make them stop or do it better. The tidy meaning is “bad in a way that cannot be changed” — a person who will not learn. Though actually, people often say it with a smile. “He is incorrigibly late” does not mean he is wicked; it means he is late again, and you have given up hoping he will change. You can even say someone is incorrigibly cheerful — not bad at all, just a habit that will not budge. It is a grown-up, slightly bookish word. In casual talk people more often say “he never learns” or “she’ll never change.”

無可救藥地