Thanks for your question.
I'm terribly sorry to hear about what you've been going through with your husband. While I can understand your concerns about giving him space, it does seem like he needs to decide what he wants. If he feels like he needs space in order to figure that out, it may actually push him away to pressure him into doing something that he doesn't want to do. It is taking that risk that he will pursue this other woman, however if he is going to be in a relationship with you for the long term, he has to be 100% comfortable with the idea.
It's a tough position for you to be in, and it can be hard to say what will come of it. Some people take some space and that is what they need to put things into perspective. At that point they can rededicate themselves to the relationship. Marriage counseling may be necessary to repair some of the damage caused by this kind of betrayal.
A lot also depends on what has caused him to start feeling like this in the first place. Some people go through personal crisis' at different points in their lives, and it can manifest itself with these types of feelings even if the relationship has otherwise been fine. Other times it can be about problems directly related to your relationship, so if you have an idea of what led up to this behavior that could give you an indication of how likely he would be to get over this with some space.
I definitely wish you the best with all of this, and if there's anything else I can do to help please let me know,