Your discussions can go in circles for many reasons. I will focus on what YOU can do, because you are the only person you control in any discussion.
One is that you fail to listen to the end. This means she has something to say, it is her priority at that moment, and you don’t listen until she is done. You interject your thoughts, and that takes away her ability to tell you what she needs you to hear.
It’s common behavior. Everyone does it.
The problem is that when two people have an issue to discuss that is as important as infidelity, the rules of discussion have to change away from "normal arguing" to listening for information, to support, and to change oneself.
You have said that you break down and cry, have shame and guilt. If you do this during a conversation with her, you take away her ability to express her own feelings - which likely also include shame and guilt (surprise!). But yours overwhelm the situation.
So the "circle" keeps happening because you take it there.
Things you can and must do to change this:
1. When she is talking, do not say anything at all. Let her speak, and let her finish the entire thing.
2. Do not speak when she is "done". Sit there and count to 50 in your head, slowly. If she is "done", she will ask you to speak. But chances are, she will have more to say to fill that silence. In most cases of conflict or negotiation, this silence will be filled with very important information. HUSH. WAIT.
3. Do not try to defend yourself. There is no defense for infidelity.
4. You cannot fix how she feels. Any attempt will fail. So, VALIDATE HER FEELINGS, even if she says you hurt her and she thinks it was on purpose, or you shouldn’t have cheated, or are an idiot for cheating. She’s not wrong, it’s how she feels. We cannot "correct" anyone else’s feelings. Remain defenseless when it comes to how she feels.
5. Stick to one topic. Don’t switch around. This results in circles because you fail to completely cover any topic, and instead just have 60 topics juggling around at once. It’s best to say at the start, "I would like to stick to the topic of _____, but know we can talk about other things later. Let’s try to get one thing at a time exposed and openly discussed." Then stick to it.
6. If the words "what about" start to come out of your mouth, close your mouth.
7. When criticized, do not respond immediately. The tendency for humans is to try to defend when criticized. Instead, try saying something like, "I need to think about that, and will come back when I have a chance to dig deeper into myself on it." Then dig.
8. When she stops talking and turns it over to you for your turn, briefly summarize what you heard her say, but in your own words. That way if you don’t understand her, she can correct that misunderstanding. Let her do that if necessary. Get clarity FIRST, then respond.
9. Be humble. But in your humility, remain focused on allowing her to express her feelings and needs. Right now, your stuff takes the back seat.
10. Resist crying. Take a 3 minute break if you need one. But this isn’t about you anymore. Your affair was about you, 100%. The recovery is about your wife.