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Courts only terminate parental rights/responsibilities when doing so is in the best interests of the child. Typically, that only applies to adoptions, regardless of the visitation situation. Even if a parent is not getting to visit a child, courts usually find that keeping someone on the hook to support the child is in the best interests of the child.
That said, if a visitation order is in place and the custodial party isn't complying with the order, a noncustodial may file a motion for contempt. The court can then sanction the custodial party for failure to comply with the court order. Further, a custodial party's interference with the relationship of a noncustodial parent can factor into a court's decision if the noncustodial petitions to modify custody and visitation.
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