Lying partner

So I've been in a relationship now for 12 years. In many ways it is great. We have a good life. Similar interests. We have fun together. Our relationship is an open on so we are free to have playtime with others. This has never really been an issue. However, as often happens in many relationships our sex life has dulled over the years. I've discovered that he hooks up quite often with others. I think what I am most upset about right now is that he does things with other guys he won't do for me. For example he says he doesn't like to swallow. However I've seen the messages where he talks about how he loves it. He has never done that for me. That's just one example I have more. I'm at the point where I am very hurt by this. And when I confront him he flat out denies it and lies and will not back down. What do I do? I don't really want o leave him but I don't want to keep going like this either...