When LockDown Browser for Mac goes into a constant "update loop" when starting the browser, we recommend the following steps:
1. Directly log into your Mac as a user with "Allow user to administer this computer" in System Preferences-Users & Groups.
2. Download a fresh copy of LockDown Browser from your school's unique download link:
where "xxxxxxxxx" is your school's unique 9-digit Institution ID. (Do not use the web address with "xxxxxxxxx". It must be the 9-digit number provided to your institution.)
3. Re-install the browser.
If the deadline for an exam is near, you may want to consider locating another computer, Mac or Windows, with LockDown Browser. There is also LockDown Browser for iPad, if allowed by the instructor.