Sometimes you have trouble saving settings in WooCommerce. Your shipping zones do not get saved or your WooCommerce Bookings resources fail to get saved. Here are possible issue scenarios for you
Corrupted WooCommerce database tables
Not being able to save may indicate damage to your WooCommerce MySQL database tables. The best way to fix this is to completely deinstall WooCommerce manually followed by a new installation. This rebuilds the database tables anew
Plugin conflict interfering
The form failing to save may be due to conflict between active components. You can check this by deactivating all plugins but the one you need. Alternatively Plugin Organizer is a more elegant way to do this check. You can use a plugin filter to deactivate plugins on a specific admin page only. I made a video tutorial on how to use it here.
Too much form data sent.
If you notice product variations, tax rates and other large data sets not saving, Suhosin (a security module in PHP) may be preventing the POST data from being saved. This issue can also be caused by servers with version PHP 5.3.9+ and servers running mod_security. To verify that you are really experiencing the issue describe in this document, you can temporarily install and activate this free plugin: https://wordpress.org/plugins/wp-max-submit-protect/
For troubleshooting information read this article on WooCommerce.com.