My W also never apologizes (to me at least, she does apologize to others).
I do apologize, and have recently tried to apologize more effectively.
My W, however, also seems to interpret an apology from me as proof that she was right all along and that therefore I was just causing her pain by arguing with her in the first place.
Recently it seems like every time we have disagreed, and then I realized we could work something out, retracted my entrenched position and apologized, this disagreement shows up in the next list of ways that I continue to be impossible to work with.
Me 42, W 39, S8, S6, S2 M 11y, A & ILYBNILWY 11/08 Walking away from a bad situation.