I think they did appeal it. The appeals court ruling was based on a procedural finding. The NBC stuff was nothing more than dicta. They didn't declare Obama or ANYONE to be a natural-born citizen or to be eligible for office. All they did was declare that the governor of Indiana cannot be legally expected to vet presidential candidates. Defining NBC accurately wouldn't create a legal obligation for the governor to vet presidential candidates. If the plaintiffs could establish that first, THEN they could try to get the courts to admit how NBC is defined.