Hi Thomas,
Thank you for writing in, yes I can see this issue on your site, but we can not replicate it on our end, the Content Area Modal element works both on desktop and mobile on our end.
Please ensure that you are fully up to date. WordPress, Theme, and Cornerstone (Version Compatibility)
Remember to clear all your caching features (plugin, server-side, CDN, and browser’s cache) after updating so that the code from the latest release is always in use. This will help you to avoid any potential errors.
If updating does not resolve it, please do a testing for a plugin conflict. You can do this by deactivating all third party plugins, and seeing if the problem remains. If it’s fixed, you’ll know a plugin caused the problem, and you can narrow down which one by reactivating them one at a time.
Let us know how it goes,
Cheers!