Patients usually sign contracts wtih doctors saying that they will be responsible for the costs of their treatment, whether or not the patient's insurance covers the cost. As a courtesy, the doctors bill the insurance carrier and are paid directly for covered treatments, and they bill the patient for the co-pay amount, which is paid at the time of the visit and isn't refundable.
If your contract with your doctor says something different, then that document governs your rights, and you need to review that document, including what it says about follow up visits without applicable co-pays, and refunds of balances after their carrier has paid for the treatment.
Disclaimer: I'm only licensed in CA. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.