Lost, Izzy is right re :
"what To date, all he's learned is the need for taking greater care to keep his future infidelities under wraps. "
That is what my h did, every time. I was having to behave like Poirot by the end, and evidence became hard to find.
Also, I do agree with PP/A re withdrawing. I did exactly this, which had always been his forte. I took my clothes to the spare room (which he had often used, against my wishes) and it really freaked him out. He started paying me compliments on my clothes etc for the first time in years, followed by angry raving emails when I didnt bite. I didnt ignore him completely, but I told him nothing of what I was thinking or doing, and said I would save it for Relate.
I actually found out afterwards that he continued sex chatting new women all that week and a half, right up to the night before we went to Relate.
I also kept an online yournal of all kinds of nonsense eg I recorded everything he told me about the infidelity, and was able to add to and refer back to it, every time he contradicted himself, and denied contradicting himself. I had a section for my current feelings. I had lists within it about my options, and made sure I looked at the advantages of difficult option such as leaving, as well as the advantages of staying. I kept lists of what I needed to do right then. And even during the Realte stage, I arranged a weekend away, leaving him with the kids, a few unusual nights out, and lots of phone chats with friends.
Meanwhile, he sat in his office, sex chatted, obsessed and stewed. For all the good it did him. And he lied to the kids, telling them I had invented everything, for which they were later furious.