Is a milk allergy curable?

It can go away: There is no "cure" for milk allergy. Usually true milk allergy is seen in babies and young children and many children may grow out of it. There are some cutting edge desensitization protocols for food allergies but these are still considered mainly experimental and are not considered cures.

Working on it: Several research protocols look very promising, primarily through oral desensitization (OIT) - in other words, ingesting increasing amounts over time. However, this risks anaphylaxis, and is not ready for "prime time". Questions remain as to whether this is permanent (thus being "cured"). However, many, many of my patients (mostly youngsters) have just outgrown it with time, and remain just fine.