Self Service Icon deleted

Did they un-ernoll their device by removing the certificates and profiles? Because I think that's the only way the icon could have been deleted. its tied to the enrollment profile and can't be removed by an end user.
If so, you'll probably have to re-enroll the device to get it back.

Is there a way using JSS I can restrict them from removing the profiles on the ipads themselves?

Truthfully I haven't used the iOS part of Casper Suite now in a few minor version changes, so I'm not sure what's been introduced lately, but from when I used it the answer was no. But not because JAMF doesn't want to be able to do it. Its because Apple's policy on this is the devices are "self managed" and they don't like the idea of an admin locking devices into a management framework, without the ability of the end user to un-enroll themselves.
While in a corporate environment or a BYOD type setup this makes sense, it makes no sense whatsoever in a lower education scenario and I always found it incredibly shortsighted of them not to allow for this.
That said, I'm not sure if Apple's Configurator allows for better management over what can and can't be done on the devices themselves. Again, I haven't been using this in a while so I can't really tell you.