Problem:
I can't update WPML after transferring the site from staging to live.
Solution:
Please try the following steps to register the production with a new key:
1. Go to plugins-> Add new-> Commercial tab
2. Click on "Unregister WPML from this site"
3. Click on "Register WPML"
4. Click on "Get a key for this site"
5. Create the production key and use it to register the site again in plugins-> Add new-> Commercial tab