A few things to check that can hopefully help troubleshoot
1) Check the permissions in both the entity the enumeration is stored in, as well as within the drop down (look at the editable field)
2) Make sure the user you are logged in as, has the correct permissions
It seems like Students should be able to see the status of their request and make requests, but not necessarily change them. Administrators are the ones that can actually change that status. I would double check that Administrators can edit the enumerated value, and then make sure the drop down is in the right place.
My best guess is that the drop down needs to be on the Admin page, and then once an Admin makes those changes, they are displayed to the Student. It makes sense that a student wouldn’t be able to edit the drop down because a Student can’t approve or reject their own requests.