Yes I have made a test site now.
I have set up a place to see the problem here: http://digiwptest.wpengine.com/wp-admin/post.php?post=12&action=edit
Try changing the date in the Fields Table and click save. The old date should still appear.
Then try to disable the Object/Transient Cache at this url http://digiwptest.wpengine.com/wp-admin/admin.php?page=wpengine-common
Try again changing the date and click save in the Fields Table. The change is now saved instantly without issues.
The issue seems to be with saving changes….
Let me know if you need anything further information from me.