Not Self Enrollment possible

Yes - First idea, would be to go to 'Global Management', and check that 'User Initiated Enrolment', for your platform (e.g. OS X) has the tick-box, check to ALLOW user initiated enrolment..

Second idea is to check: (in Casper) System Settings, JSS User Accounts & Groups, Privileges to see if you have set ON allow Enroll computers and Mobile Devices - you might have, or intend that restricted to a tech group.
it Needs to be 'ON' for those individuals or groups, who should have this right.

It also could very likely be due to the changes in iOS for untrusted certificate issuers. Is your JSS using an SSL certificate created using the wizard in the JSS? If so, this is likely it.

If your going through User Initiated Enrollment with built in CA created SSL cert and you don't back out of the enrollment process after installing the CA and go to Settings > General > About > Certificate Trust Settings and do the manual trust it will fail.

If you are going through DEP or Configurator and supervising it automatically does the extra trust settings.

You can read more about these changes and the steps needed to resolve them here: Changes in User-Initiated Enrollment with Untrusted Certificate Authority Signed SSL Certs
and
Enhancements to certificate security for mobile device management (MDM) enrollment