Hello @oisin,
I have checked your site and I can confirm that you are still using Cornerstone 1.3.0. That latest version of Cornerstone 3.4.6 is now available in automatic updates! This release contains fixes for several issues so be sure to check out the changelog (https://theme.co/changelog/). Please do update to the latest version. After doing the updates, always remember to clear all caches when updating so that the code from the latest release is always in use. This will help you to avoid any potential errors.
Automatic updates does not mean that Cornerstone will update it self. You will still go to the plugins section or in Dashboard > Updates and do the updates. You may not be able to update Cornerstone is you haven’t validated Cornerstone. You must make sure that your license code were assigned to the site and then validate Cornerstone. Please also be advised that only Cornerstone license code is needed to validate Cornerstone. You cannot use X theme license to validate Cornerstone and vice versa.
Since you are using an older version of Cornerstone, I would recommend that you create a staging site. This is very useful because you can test drive any updates in the staging area, do the customizations and troubleshooting without disrupting your live site. Once everything is perfect, you can easily and flawlessly proceed the update in the live site. To know how to create a staging area, please check out these articles:
And lastly, please ensure that you have meet the requirements to run the latest WordPress 5.0.3 which needs at least PHP 7.2. You can check out the rest of the requirements from here: https://wordpress.org/about/requirements/
Please let us know how it goes.