Do good fathers have a chance, after a relationship has gone sour?

Many times we hear of the "deadbeat " comments towards men, who are not providing for their children. We often hear of women with a child or children, angry by his inability to come around, call, or even acknowledge the child is indeed his. I want to discuss about the good fathers, the ones who want to do right by their children, but because of the failed relationship with the child's mother, they are not given the opportunity. So my question is do good fathers have a chance, after a relationship has gone sour? Lets discuss.