Classroom not appearing in settings

I accidentally removed one of my class iPads from the Classroom app. I can't add it back unless I create a new class. Why?

The removed iPad will not show the Classroom option in settings. I remember a few of the iPads doing this when I first set up the class with all my (shared) iPads - it took several goes to get them all joined because the same thing happened. It seems like after one attempt or one successful connection, that iPad can never even attempt to join the same class again.

Is this a known issue and is there a solution other than starting again?