Thanks for your reply. REST API is still showing "No" on the staging site and I don't think Automatic Translation will work on the staging.
But anyway, could you please check your production site and navigate to WPML > Support, Scroll down to Advanced translation editor, and click on Error logs, Please share the last 3 logs with me.
It looks like there are some permission issues. Please try the following steps after a backup and check if it helps or not
1) Visit WPML.org>>My Accounts>>Sites - https://wpml.org/account/sites/
2) Delete the existing site key
3) Then create a new subscription key for the site
4) Visit the Site Dashboard and go to Plugins>>Add New>>Commercial
5) Click on the *Unregister WPML from this site* button
6) Register with the new site key and refresh the page
If the issue exists, please share both WP and FTP access here to your production site and I will escalate this to our 2nd Tier Support for further assistance.
I apologize again for the delay and the inconvenience.
I've opened a report and our 2nd Tier Support will look into this for you. Please make sure that the login token still works for another 2 - 3 days. I will come back to you once I've feedback.