You will continue to see the checklist for your current day until the end of the day. The default time for this to happen is midnight, unless you have set a different time. This allows you extra time to add notes for the day.
*Make sure you have added your progress pic. The daily progress pic is one of the required tasks. It will not move to the next day until you have completed that task as well. To add your progress pic, tap the camera icon next to that task on the list.