One of the first things I learned in Psychology class was that a person's past behavior is a very good indicator of his future behavior. You must have heard that once a cheater, always a cheater. That is especially true when his spouse shows that she is afraid to divorce him. What usually happens is that you end up looking the other way because the alternative is not attractive to you. You have already emboldened him to cheat by allowing it over and over again with no more than an argument for his months of pleasure. A fair trade in his book.
I cheated 4 times before my wife decided to open our marriage. I was not going to change. I have always had more than one women in my life and marriage did not change that. We got involved in some group sex and then threesomes. We ended up sharing a girlfriend for 30 years. My wife and I agree that had we insisted on monogamy, we would have divorced a very long time ago. There is a whole science of human evolution and how we are one of the few species who have sex for non reproductive reasons. We are attracted to others and there is no stopping that. How we act on that attraction varies from person to person.
I kept on cheating because I knew that my wife loved the lifestyle I was providing her and as she said, what the eyes do not see, the heart cannot feel. There are both husbands and wives who look the other way as long as their spouse is discrete. You indicated that you do not desire a divorce so you have taken away your main weapons. You are left with very little else to deter your husband. I would gladly trade an argument for some good sex for a few months. If I was facing divorce I would think twice about it, but it seems that even that does not deter some.
Here is an article that describes how my wife and I put our marriage ahead of monogamy. Worth a read:Rethinking monogamy today - CNN.com
We know lots of married couples who have saved their marriage this way. Our girlfriend is married and in an open marriage. They are married longer than 25 years. We are married for 44 years. We don't go out on weekends looking for new sex partners. In fact, my wife and I had less then 10 sex partners combined, and half of those were as a couple. When you know that your spouse can also see others it changes the ballgame and makes you step up your game. Good luck.