Well here's the deal... if you intend to keep this going, then you need to understand that if you forgive this woman, then you can never bring it up ever again, for the rest of your life.
If every time you have an argument, you are saying "yeah well you had an affair!", then you haven't forgiven, and you are just torturing her. That's wrong.
You can't do that.
I gotta be honest with you... my wife starts screwing other men and gets pregnant, I'd divorce. Just being honest. I'll move on and find a woman that wants me. Obviously this one didn't, and I'll let her go find whatever guy she really wants. I'm moving on.
But... if you are a better man than me, and you want to give it a shot... ok. Go for it. To me, if she can do it once, and lie constantly to my face.... then I think she'll do it again.
The only thing I would advise you to do is.. examine yourself. Many times, it takes two to tango. Usually when one person runs off to get their sexual/relational needs met by another person, it's because they were not getting met at home. Not always the case, but examine how this happened, and what led to this person finding their needs met elsewhere. Maybe you did the best you could, and she just did this on her own. But if there is some part that was on you, own it, learn from it, and don't repeat it again.