Hi there, I responded to the support ticket that you opened regarding this issue. I wanted to also respond here in case any other users had the same problem.
There was a brief issue with how the image for Facebook was being set in a site's code, that affected sites where the user had recently uploaded a new header. Your site's theme, Chateau, is configured to use the featured image of a post as the header so in a sense, you upload a new header with every post.
Your report helped us to troubleshoot the issue and get it fixed. Thanks! It's back to working the way it was before, which is:
1. If a post/page has no featured image or uploaded images, Facebook will display the Blavatar as the thumbnail.
2. If a post/page has a featured image, Facebook will display the featured image.
3. If a post/page does not have a featured image, but has images uploaded into the text area, these will be selected by Facebook -- up to 5, in the order of most recently uploaded. These images must be uploaded directly, not inserted via the URL or Media Library tabs.
Finally -- once a page has been shared on Facebook, the images Facebook found on its first look are stored in a cache. If the images on the page are changed, Facebook doesn't check until the cache expires (which is unpredictable, can take days or weeks).
There's a way to force Facebook to check again, which is to use the Debug tool mentioned above. Copy the link of the post and paste it into the blank of this page, then click the Debug tool:
This also works to update the page's text excerpt displayed by Facebook.