A recent Avvo post caught my eye, as the issue raised by the mother is one often misunderstood:

Can a father who owes $25,000 in child support see his child even though he has been absent for 12 years? The biological father of my child is seeking visitation, but has never paid child support although there is a court order, and my daughter does not want to see him.

Support and visitation are supposed to be separate issues. That said, 25k is a lot, and I expect that a judge would certainly ask what the father is doing in that department. The age of the child is the most important issue here. The child does have a say in things, but the weight of that is relatively minimal. That is, until it’s just about dispositive after 16. Anyone involved in such a situation should seek the advice of a local attorney.