I think it depends. If you mean "stay with" as in try and work out a relationship that you know already will fail; no. but if you can live together in a platonic (sp?) kind of way and both see other people but parent your child I know more than one family that does this and it works well for them.
Don't let guilt get to you...better yet, don't even feel guilty. Things will be perfectly fine, I promise! My situation is a bit different because I was married and left when my son was 3 months old. It turned out perfectly and now I have been with current SO for almost 3 years now and have never been happier
No, I wouldn't stay with him for that reason and that reason only. I'd rather my LO be in a loving, happy environment with one parent at a time, than be in an environment where their parents are together but can't get along or trust each other.