For a while now we've seen reports of the builder previews in Cornerstone and Pro not working in SiteGround staging environments. If you've updated to Pro 1.2.5 or Cornerstone 2.1.5 or later, you'll be able to more clearly see the symptoms as the error messaging was improved.
The problem is that the page builder is trying to preview using the production URL, even though it's in a staging environment. SiteGround's staging environment primarily works by using a copy of the production database on the staging install, and rewriting HTML output to include the staging URLs. This works for most intents and purposes, but leaves a few cases where site URLs don't get replaced. We've discussed this at length with SiteGround, and they've let us know they are working on a new staging system that will address the issues that have been uncovered. Meanwhile, they've offered a workaround to help users experiencing the problem. We've added their recommended solution to this article (towards the bottom): https://theme.co/apex/forum/t/troubleshooting-builder-preview-warnings/14404