[Waiting for user feedback] WPML translation issue with the Product translation not saved after translation

Please let me know once you have run the clean up steps. It also would be helpful to enable the debug log to see if there are any background errors happening.

WordPress includes a debug mode that helps reveal PHP problems. Let's enable this and see if there are any errors we can locate.

To enable it, open your wp-config.php file and look for

define('WP_DEBUG', false);

Change it to:

define( 'WP_DEBUG', true );
define( 'WP_DEBUG_LOG', true );
define( 'WP_DEBUG_DISPLAY', false );

In this case the errors will be saved to a debug.log log file inside the /wp-content/directory.

The wp-config.php is located in your WordPress root directory. It’s the same file where the database configuration settings are. You will have to access it by FTP or SFTP in order to edit it.
If you open wp-config.php and that define statement is not there, you can add it right before this line:

/* That's all, stop editing! Happy blogging. */

Please note that you’ll see everything, not only related to our Plugins. This will most likely include messages from other plugins, your theme, and sometimes even WordPress core. The messages appear all over the place.
Sometimes they appear right on top, but they can also appear in the middle of the page.

DOC:
https://codex.wordpress.org/Debugging_in_WordPress

After enabling the debug mode, please try to replicate the issue. Navigate to the page where the error message being displayed. The errors will be either displayed on the screen or logged in the debug.log log file inside the /wp-content/directory.

Paste the latest lines here. No need to paste the entire log file, just 50 lines or so will do. Please censor any sensitive information.