Does the band at 18 kDa have fuzzy edges and is the expected mass at 12 kDa based upon any glycosylation?  I have seen the phenomenon you described a few times but usually for smaller molecular weight proteins under 10 kDa and with a reversed band morphology.  You are correct about the gel shift phenomenon upon reduction and a Stokes radius change but the SDS/protein mass ratio does not always follow when the protein is not and average protein. The ratio of SDS to protein is also influenced by acidic and basic amino acid content, high hydrophobicity, glycosylation, .   

Another possibility is that there is an internal clip where the resulting peptides are held together by disulfide bridges (assumed the protein has disulfides because you described reduction).  One of the peptides may be too small, under a few kDa,  to see on the gel but the remaining peptide is at 15 kDa.  If you run N-terminal amino acid sequencing and there's no glutamic at the N-terminus then you should see two N-terminii if there is a single clip, right?  There are some other possibilities but you might consider these firstly to begin the diagnosis.

Hi there,

Are you sure your protein isn't dimeric in its native form maintained with both intrachain and interchain cystin bonds? It would run 18kD instead of 24kD because of the possible presence of these internal cystins resulting in protein compaction. And would run 15 instead of 12kD in reducing condition (running higher MW than expected is often observed).

How is your protein normally charged? Is it rather cationic or anionic? What is the pI? For proteins, and even on SDS PAGE, this makes a difference for band height in SDS gels