When a parent who is supposed to be paying child support falls behind on making the payments, this can place enormous strain on the already difficult relationship between former partners who are now separately parenting a child together. Sooner or later, the desire to compel the owing parent to get one's act together and pay the child support will probably inspire the idea to withhold visitation privileges. While this may seem like a reasonable form of leverage, anyone who is thinking of taking this course of action should absolutely reconsider.
The primary reason to reconsider withholding visitation to compel another parent to pay owed child support is because visitation is just as much the right of the child as it is the right of the parent. Ultimately, on a personal level, you want the best for your child. This is why you want the other parent to follow through on his or her responsibilities -- for the sake of your child. While you have many responsibilities as a parent, it is unfair to take away a child's right to see his or her other parent simply because the two of you are in a conflict.
Beyond the personal reasons why this is inadvisable, the law is almost certainly not going to treat this behavior with sympathy. Each state has a suite of options for how to compel a non-paying parent to make good on his or her obligations, and the court expects the parents to operate within the law when pursuing owed payment as well as custodial fairness. The courts treat visitation rights and child support obligations as separate things, and may not take too kindly to you conflating the two. Even if you feel that you have the moral high-ground, refusing visitation to a parent who owes child support may cast you in an unfavorable light to a judge, and which may actually work against you in the future.
It is completely understandable to feel that something should be done to compel an owing parent to pay, and you are right -- something should be done. That something, however, should not be to punish the child for a parent's mistakes. If you need further guidance on how to pursue child support payment, an experienced lawyer can help you work within the law to reach this goal.
Source: About.com, "Can a Parent Withhold Visitation For Unpaid Child Support?," accessed Oct. 07, 2016