Azide prevents cells from using ATP to get things done. In some cases binding of antibodies to antigen may cause the cell to aggregate and internalize the antigen. CD3 is a classic example of antigen capping, so called because of the way the process looks with fluorescence microscopy. This process requires energy and is prevented by the use of azide and/or cold (4°C).
I'm not aware of any direct effect of azide on the actual affinity of the
antibody for the antigen. Unless the epitope undergoes some energy-requiring conformational change - haven't heard of such a thing.