In Magento 184.108.40.206, when I go to System > Configuration > Web > Secure and set
Use Secure URLs in Frontend to Yes, when I click Save, the field is set back to No.
There are no entries in the logs when this happens and there are no relevant script errors. I note that it says "Store View" next to the settings, however I've looked at the store views and website settings and they all say use the Default.
I also see the same problem with
Use Secure URLs in Admin.