I was your wife. I had a PA (hers was just EA? Is this definite? I originally claimed that myself) and then spent the next few years 1/3 in 2/3 out. I fantasized about getting out, dating OM out in the open, looked for places to live, etc.. all while going to MC and giving halfhearted attempts at fixing our M.
Deep inside there was something holding me there but I didn't know what it was. I couldn't find it within myself (or didn't really want to, I guess) to work on our M for anymore than a month or so at a time. Just like your "business encounter sex", my H could tell that I was just going through the motions. Yes, there were times it was more than that, but not always.
She doesn't know what she wants. She isn't totally out but she isn't really in. What will change that? I don't know. For me, I know that my H being silly with me, making me laugh, trying, reading books, wanting to talk did not do it. It made things better for short periods of time but didn't really change how I felt inside and that was exactly the way your W felt. I wanted SOME passion towards my H and I didn't have any.
It wasn't until he became the WAS that I was ready to look at myself, do the work and try to save our M. I am very lucky that it doesn't appear to have been too late, time will tell. I am not suggesting you leave her, this is something that you will feel inside - that you are just fed up with the way things are and you refuse to do it anymore.
I LRT'd for several months before my H came back and even then, the first 2 months were pretty shaky. I did not contact him at all unless it was about the kids. I was always nice but didn't initiate conversation and ended it a lot earlier than I would have previously. I didn't ask him to get me things I needed, I went and did it myself. I basically pulled away while being friendly and co-parenting. Take it for what it's worth because it is only my personal opinion, but I don't believe that continuing to initiate sex, keeping the status quo and act like all is well is going to be the way to fix this.
M 46 H 44 D 12 S 8 M 9 T 11 BD 2/15/13 "Makes sense to stay together" 5/12/13 Agree we are 'healing' 7/13 Definitely Piecing 9/13