In Missouri there are two ways a person can face jail time for not paying child support. The first way is through the criminal justice system where she can be charged with a felony or a misdemeanor crime. The second is through a civil contempt process. Your question doesn't indicate which route they are using to help you but your description is similar to a criminal non-support charge.
If she is being charged criminally, then she is appearing regularly in front of the criminal court as part of the criminal process and the case will keep getting continued until the matter is set for trial or she enters a guilty plea. Criminal defendants are presumed innocent until proven guilty. The delays are part of her due process rights being protected and it might be getting continued for her to have an opportunity to get a lawyer.
Since jail time is a possibility ... she has a constitutional right to an attorney is both criminal cases and contempt matters but the court doesn't have to give her time for ever...just sufficient time to be satisfied that her rights are being protected.
Remember, the Clay County prosecuting attorneys are not your lawyers...they represent the state. Missouri allows the prosecutors to go after your ex wife for both criminal non support and contempt charges but they won't protect your rights as a "victim" or a custodial parent.
I strongly urge you to seek counsel to ensure your rights are being protected. Good luck.
The Family Law Group, LLC