Hi Alex, this sounds like a very co-dependent relationship. You feel the need to save him - to make everything right. That isn't your job.
The fact is he is treating you horribly. Each time he does this, you feel less and less. Well, that's probably because each time he does this you feel like you deserve less and less. After all, if you deserved a partner that loved and respected you, he would have stopped, but he hasn't. So, maybe this is just your cross to bear.
Alex, if you can be respectful and loving, then you deserve someone that treats you in the same manner. Right now you are with a very selfish master manipulator. He is only interested in himself and his feelings. The way he is pouting because you're upset proves that. He's saying that you have no right to feel the way you do, and that he is going to treat you poorly until you get over his infidelity. That is horrible Alex, and it's emotionally abusive.
He has cheated 6 times. How many times does he get to cheat before Alex leaves for good? What is the number? It isn't 6, so is it 8? 12? Will Alex never leave? Because if you aren't going to leave, you might as well stop getting upset and bringing it up. He's showing you he won't stop, and you're showing him that's ok.
I'm sorry - I'm sure these comments are not what you're looking for. Unfortunately, saying that he's mean and that 'we're here for you' isn't going to help you. Getting you to realize that this is not normal and that you do not have to accept it is supporting you. Anything else is really helping you stay in an abusive relationship.
Be strong Alex - realize you deserve a better partner. Leave this cheating manipulator and build a real life for yourself.
And what is this man teaching your children? What kind of example is he?