In my experience, most of the antibodies have worked after several freeze-thaw processes, but in general and depending on how often you are going to use the antibodies, it is recommended store them in small volume aliquots to avoid damage due to these repeated processes.
Repeat freeze-thaw cycles can denature the antibody causing it to form aggregates thereby reducing its binding capacity. You can use the repeatedly frozen secondary antibody for 4-5 times max.
Usually, the secondary antibody is stored in aliquots for one time use in - 20 degree C to avoid freeze-thaw cycles. But enzyme - conjugated antibodies should not be frozen but kept at 4 degrees C.
If the secondary antibody contains the cryoprotectant like glycerol in the buffer to a final concentration of 50% it could prevent damage done by repeated freeze-thaw cycles.
Repeated freezing and thawing of antibody should be avoided as this may result in degraded functionality. As an alternative, you may freeze reconstituted antibodies in single-use aliquots or add antifreeze (Glycerol or Ethylene Glycol) so that the stock solution can be maintained at -20°C in liquid form to enable pipetting without thawing. The use of glycerol inhibits formation of damaging ice crystals by keeping the antibody in a liquid state.