The Deluxe combo Federal and State version should allow you to prepare multiple Federal and multiple Arizona returns. So I'll assume you started a brand new tax file for each of your children. Then after completing each of their Federal returns you continued on to the State Taxes tab to prepare a state return, where you encountered the problems.
Are you using the Windows version or Mac?
Run your program updater to be sure you have the latest updates, then restart your computer.
If you still have problems after that, and if you are using Windows, you can try running a repair:
https://ttlc.intuit.com/community/bugs-and-error-messages/help/how-to-repair-turbotax-in-microsoft-w...
