If the protein is His-tagged, load the purified protein on to a Nickel column and place the column in a water bath above the protein's melting temperature. Recycle 5mls of water through the column to collect the peptide and then dry freeze or speed vac the sample to concentrate the peptide.
I have seen this done for peptidoglycan fragments: Peptidoglycan Recognition by Pal, an Outer Membrane Lipoprotein Biochemistry, 2006, 45 (7), pp 2122–2128 I cannot see why it should not work for peptides. Don't forget if you are going to run a gel of the peptide to use tricine gels. Dan