Yes, sometimes. The chances of a child outgrowing food allergies depend on several factors. One is the type of food the child is allergic to. A study found that 79% of children outgrew dairy allergies by the age of 16. Children with egg allergies have a greater than two-thirds chance of outgrowing their allergies by late adolescence. In contrast, only about 20% of children diagnosed with peanut allergies, and 10% of those with tree nut allergies, ever outgrow their allergies.
Another factor that has been strongly associated with outgrowing food allergies of several types is specific IgE levels. The lower the levels of allergen-specific IgE detected in blood tests, the greater the chance the allergic patient will eventually outgrow the allergy.
Studies have found that allergies can be outgrown well into adolescence. Your allergist will have specific recommendations for monitoring your child's chances of outgrowing his food allergies. They will likely involve measuring his allergen-specific IgE levels through blood tests. And, if those numbers look favorable (and if your child has had no other signs of still being allergic to his allergens), conducting a double-blind placebo-controlled food challenge to determine whether your child has developed a tolerance to his allergens.
Sources:
Savage, Jessica H., et al. "The Natural History of Egg Allergy." Journal of Allergy & Clinical Immunology. Dec. 2007. 120(6): 1413-17.
Shek, Lynette P. C., et al. "Determination of Food Specific IgE Levels Over Time Can Predict the Development of Tolerance in Cow's Milk and Hen's Egg Allergy." Journal of Allergy & Clinical Immunology. Aug. 2004. 114(2): 387-91.
Skripak, Justin M., et al. "The Natural History of IgE-Mediated Cow's Milk Allergy." Journal of Allergy & Clinical Immunology. Nov. 2007. 120(5): 1172-77.


