You have to file the appropriate papers with the court and demonstrate to the court why it should stop the child support. Normally the court balances many factors including, but not limited to, both spouse's earnings, who is the primary custodial parent, what the child's needs are, what is in the best interest of the child, other financial resources, special needs of the child, whether the other spouse is living with someone else who is also providing financial support, in making such a determination. The courts normally want both biological parents to contribute to the upbringing of the child and to actively participate in child rearing responsibilities. Without the benefit of having all of your facts, it is not possible to say whether you have a valid reason that the court might agree with. You really need to consult with a family law attorney to go about this properly.
Disclaimer: It is impossible to evaluate a legal problem without a comprehensive legal consultation and review of all the facts and documents at issue. Consequently, this response does not constitute or establish an attorney-client relationship but is offered for general informational purposes only. Laws differ from state to state and each case turns on facts specific to the case and parties thereto, thus this answer does not constitute legal advice, and should not be relied upon as anything more than a starting point or suggestion that the questioner seek professional assistance from a practitioner in your state or county/parish, practicing in your area of law.