IgA is one of the types of antibodies the immune system makes. Some people have an error that causes them to be unable to make enough IgA. So when these people are tested for IgA antibodies to something specific, such as gluten or gliadin, the test comes back negative because their body is unable to make enough antibodies to the gluten/gliadin to show up on the test even if they do have Celiac.
To make sure this isn't an issue, ask your doctor for a Total IgA test.
For more info, check out neurotalk.psychcentral.com/archive/index.php/t-105601.html
- excellent discussion of testing for Celiac in light of selective or total IgA deficiency...