From an excellent resource about far more than just our topic,
http://www.health-spy.com/foodallergy.html
If one has an non-IgE-mediated immune system sensitivity or response to certain food types, e.g. Gliadin or Dairy, and one eliminates these food sources from one's diet, i.e. one goes on a Gluten-free or Milk-free diet (and does not consume any hidden sources of Gliadin), then the production of the IgA antibodies corresponding to these food types does not go down immediately to lower levels. Of course, without these particular food sources in the GI tract, they have nothing to attack (often besides the digestive tract itself), but the body still produces them as it is 'expecting' them. Research shows that these antibodies continue to be produced in the digestive tract (and possibly elsewhere) for up to 1-2 years after a person has ceased consuming the corresponding food items. The levels of the corresponding antibodies in the blood tend to drop off more rapidly, in 3-6 months typically. Controlled reintroduction may be one method of adjusting to these proteins without the production of these corresponding antibodies, as may low dose immunotherapy. However, if one starts to eat these food sources in copious quantities in a non-systematic and uncontrolled manner, then the levels of the antibodies are likely to increase to their former levels very rapidly. It may vary according to the individual of course, and a 'Gluten challenge' may not necessarily guarantee immediate increase in relevant antibody levels for detection if Gluten is reintroduced heavily for 1-2 weeks.