I have also experienced similar to this - I caught my husband still emailing and texting his AP, he also described it as minimal. He said there was nothing romantic about it. I started a post about it on this site and TimT gave me an excellent response which helped me reach the decision to leave the marriage.
He explained that any ongoing communication with the AP, in whatever form, is still participating in affair behaviour. They are still keeping secrets, doing something they know is wrong, and maintaining some form of emotional connection. All the time they are involved in that they are not committing 100% to the marriage or helping you in your healing. It also leaves the door wide open for the affair to start up again, whether that is there intention or not, it leaves the possibility there.
This situation has been my life for the last 2.5 years, my husband ending the affair, a few weeks of putting in some effort to the marriage, then connecting with the AP again, entering back into the affair. This pattern happened over and over again. I realised he was never going to end his relationship with her, even though we had been going to counselling for 5 months. I knew I had to be the stronger person and end this pattern, because it had taken over my life. He moved out on Friday.
I do wonder now whether his affair was an exit affair, but when it came to it he just wasn't brave enough to walk away. It says a lot that he couldn't do what I wanted for 2.5 years (end the affair) but as soon as I ask him to move out he has gone. I know he has been to see the AP several times even though he claims the affair is over. Not sure why he is still lying to me even now!
Thx for your reply. The question I have is how would you act towards your WH each time you discovered he betrayed you again and then begged to stay married. Upon discovering new lies from my WH, I don't want to even see him. I can't imagine being loving to him.