I’m trying to add courses to a course group but each time I save the course group and come back the courses I added disappear. Why aren’t the courses saving?

Course groups do not allow you to add courses to the list if the course group is currently being assigned. The UI will look as though your additions have been added, but they won’t be. To be able to add courses to a course group that’s been assigned, you must first unassign the course group from everyone it’s been assigned to.