We all do things we regret, its does not make us mad people. Anything is possible so yeah your marriage may survive or it may not. When people we love hurt us especially our spouse we take it harder than i think we do from anyone else.
I think he is trying really hard, but i think he has it doubts and your relationship is dissolving really fast. I dont think that when someone cheats on you, you just get over it, in fact i dont think we ever get over it, its always in the back of or mind whether they will do it again. And sometimes we continue on with the relationship because we love the person, and where not strong enough to leave, but slowly over time the doubt in our mind and all the other issues they make life realy hard and eventually it gets too much and we leave, or these issues slowly destroy the relationship.
As someone said staying married for love is almost as silly, as marrying for love. You can love someone with all your heart yet not be able to translate that into a happy relationship.
Good luck though and i hope you too work it out!