My daughter and her youngest went through this; the baby was having a reaction to [something] being passed to her while breastfeeding. Daughter went through allergy testing, then was placed on an elimination diet. As foods were re-introduced, they watched the baby for reactions; turns out there were multiple allergies.
The doc felt that some of these allergies would gradually abate because the levels of antibodies were fairly low, so after a couple of years, the allergist did a controlled challenge in his office. It lasted pretty much the entire day.
He took a blood sample, then administered a minute amount of the food. He continued to watch and test for reaction as more and more of the food was given.
This was a pretty exhaustive process and it was decided that, for at least a few of the foods, the allergies had indeed 'gone away'. However, she was told to feed them in moderation. That's been a few years back, and so far there have been no further problems.
These links explain it better than I did