Blackrook, I can only tell you what would (and did) work with me; I make no claims to its efficacy towards your wife!
My husband lost a lot of his interest in me and, unfortunately, did not even miss it enough to do or say anything about it. I was the one who had to bring it up, suggest a plan of action, stay "on top" of it and not allow us to backslide, keep the R and sex talks going, all this for over a year! It was/is exhausting but the results are that we are finally getting back on track. It is a wonderful and exhilarating feeling.
Now back to your apology question. There really are not enough words in the English (or any other) language to properly make up for sexually rejecting someone. Seriously, words will NOT do it. The only thing that filled that gaping hole in the middle of my chest was action. I needed to see action from him, and pronto. Yes, he had to move out of his warm little comfort zone and move over into my world.
After about 6-8 months of increased frequency combined with lusty looks, comments and just a general appreciation of me as a WOMAN (not a friend or companion) started to melt the icy wall that I had built around myself.
If lack of sex has caused your rift, it only stands to reason that she is going to need to see some serious efforts in this area before she even considers staying. I don't know the particulars of your situation and I hope that it hasn't gotten to the point that she refuses any affection from you.
So, that's my answer. Sexual attention. Not hugs and pecks and cuddles, but sexual attention. That was the only thing that made me realize that he was serious about keeping me. He did something that was exceedingly hard for him (stepping outside the comfort zone) and you know what? He likes it! He is good at it! He is as surprised about that as me...I didn't expect that he would enjoy it, I really anticipated that he would do it 'for me', ya know?
We are currently enjoying a great period of our marriage. He has made lasting changes and proved to me that his love and desire are real--something that words alone could never have done.
