While I am not licensed to practice law in your State, I will attempt to give you some guidance here. In most States, there is no fixed "default" period of parental rights (or obligations). While you could probably file a formal application with the Court to terminate his parental rights, I would not recommend doing so, especially if there has been little or no contact. I would let sleeping dogs lie. Furthermore, there is the possibility that your daughter may wish to attend college, which is extremely expensive these days. Even if her father has not exercised his right of visitation, he would not be relieved from his legal obligation to contribute to her support at that time, or even now for that matter.
There really is nothing you can do unless you want to take the offensive here and file an action to establish paternity, custody, parenting time and child support. It certainly might be opening up "pandora's box." I would always encourage a child's relationship with the other parent because it's usually in her best interest. It's hard for her and she does not need to know what's really going on.