Hi,
thanks for the account details! I was able to log in and could reproduce the issue.
The reason for the problem is the plugin “Smart Post Lists” which is written in a very bad way: It adds its JavaScript code to all admin pages in the WordPress Dashboard, instead of only on those pages where the functionality is needed. Due to that, the save functionality is interfered with in TablePress.
My suggestion here would be to contact the developers of that plugin and ask them to fix their plugin (by loading JS code only on pages where it’s necessary, and never on other plugins’s screens).
Meanwhile, a temporary workaround could be to deactivate the “Smart Post Lists” plugin whenever you plan to edit tables.
Regards,
Tobias