Did you change the form back to using the featured image (instead of the custom "primary image" that i changed to)? I changed my site as I thought you had it downloaded and I need to get users testing to use the custom "primary image" which has always worked. It's only the built in "featured image" that had issues. Let me know and if needed I can try again but still was happening last I checked.
I'm still seeing the same issue. Edited the post hidden link
Added a featured image and saved. Edited again and the featured image is there. Saved again, and the featured is gone. It adds if you add it but disappears if I simply edit and don't do anything to it (and it's already got one).
Well you're welcome to try some more but at this point I need to launch. Were you able to reproduce the problem locally? I still don't get it but just going to survive without it so we don't break the live site at launch tomorrow.
Here is a video of my testing of your site locally here. hidden link
From what i can see the issue doesn't occur at all. The featured images are not getting removed when i've edited the page.
I suspect that something regarding your server may be causing the issue since it doesn't appear at all on my end.
For now your workaround where you use a custom field will work fine. You can continue to use this workaround should you so choose to as it won't affect your work at all since a Featured image field will just be another image field essentially.
However if you're able to check the PHP logs for your website you can check and let me know if you're seeing any errors at all that could give us a clue to what is causing the issue.
Normally we do not debug issues that are server related but if it is a clear error I can point you in the right direction. As the issue doesn't occur for me on your exact site here locally I wouldn't be able to escalate this for further checks.