It MAY be possible to transfer the reciprocity fee, but it is not a sure thing. Write the Argentine embassy in the US with full details of old and new passport numbers . See this from the fixed sticky thread above, from the Argentine embassy in the USA : http://www.embassyofargentina.us/embassyofargentina.us/en/consularsection/tramites/reciprocityfee.html
The US immigration service and homeland security would not be so helpful. At least the Argentines TRY to be helpful).
"This is my second trip, how do I know if the previously paid Reciprocity Fee is still valid?
Fees paid after December 2009 are valid for ten years for US citizens, and you do not have to pay the fee again.
Most probably, the receipt is stamped in your passport. If you are not able at all to get a copy of it, please email us at consular@embassyofargentina.us"