Fluorochromes are covalently bound to the antibodies to form stably labelled molecules. This paper describes it in great detail, from the abstract:
> Fluorochromes can be covalently conjugated to antibodies through reactions with thiol or amine groups. Typically, fluorochromes containing isothiocyanate, succinimidyl ester, or sulfonyl chloride reactive groups are conjugated to amines on the antibody molecules.
These covalent bonds are stable at room temperature and are also at -20°C. It's more likely that repeated freeze-thaw cycles damage the antibody.