Mo. Rev. Stat. § 545.910: When state not entitled to further continuance.

If, when application is made for the discharge of a defendant under either section 545.890 or 545.900, the court shall be satisfied there is material evidence on the part of the state which cannot then be had, that reasonable exertions have been made to procure the same, and that there is just ground to believe that such evidence can be had at the succeeding term, the cause may be continued to the next term, and the prisoner remanded or admitted to bail, as the case may require. If the defendant shall not be tried before the end of the term last mentioned, the state shall not be entitled to any further continuance of the case, and the prisoner shall, if he require it, be discharged.