Many purified proteins can be repeatedly frozen and thawed. The freezing process should be very rapid to avoid separation of solutes from water. The protein should be stored in small aliquots (100 µl or less) so that the freezing will go quickly. The tube containing the protein can be immersed in liquid nitrogen or a dry ice-ethanol (or acetone) bath. I use a powdered dry ice bath. The aliquot should also be thawed quickly and kept on ice once thawed. For quick thawing, I just hold it in my hand until it thaws, then mix it gently.
I'm not sure what effect boiling has on the BCA assay. It probably just causes it to go to completion much faster than the usual method of incubating the samples at 37oC for 30 minutes. As long as the protein does not coagulate, the assay probably still works. You will be able to tell from the standard curve whether the assay works with that treatment.