If you are using a commercial anti-D reagent as your starting material, you might be creating your own problems. Most reagents are now monoclonal and as such they often have very peculiar formulations (additives, diluents, etc.) that ensure their stability. When end users dilute or otherwise modify the reagents, they may lose the key element required for reactivity and/or stability (even when frozen).
I suggest you try a polyclonal (human) source (which is probably what Malcolm's group is using). If you need to dilute it to get to the desired reactivity, I recommend using either inert normal human serum or 6% BSA. Both diluents should maximize your chances of stability, either in the liquid state or frozen.