What do you do when the noncustodial parent has stopped paying third-party medical insurance premium for their child?

It depends upon how the court order is Worded. If the non-custodial parent is responsible for health insurance for the child, then you would need to go back to court. If he is responsible for paying the medical bills, then you would send him the bills. In any case, he remains on the hook for the child's medical bills.