Child support and visitation are legally separate issues in Texas — you must keep paying court-ordered support even if you’re being denied visitation, and the other parent’s access to the child generally isn’t supposed to be conditioned on payment either.
Penalties for falling behind on support can include license suspension, seized tax refunds, denial of occupational licenses and state loans, referral to collections, credit reporting, and jail. Texas also charges interest on past-due support, currently 6% per year (it was 12% before January 2000).
If you’re being denied visitation despite paying support, that’s a separate enforcement issue — talk to your attorney about filing for enforcement of the visitation order itself.