The One Click Update option will not work on a test / local / staging site since it cannot check the license.
Please Note: A WishList Member license key can be used to activate WishList Member on a test / local / staging site (list of allowed URL formats available here), but it will not count against the WishList Member license total. Some of the test / local / staging URLs won’t require the License Key to be entered.
You would need to update through FTP or by deleting the WishList Member plugin from the WordPress Plugins section and then installing the new version of WishList Member. (or just installing the newer WishList Member over the existing WishList Member in the WordPress Plugins section as the latest versions of WordPress allow for installing a new plugin over an existing plugin).
All WishList Member settings, members, etc. are stored in the WordPress database so that would be retained during this process.
That being said, we do recommend a site back up before any plugin updates in case you run into an unexpected issues and want to roll back.
You can download the latest version of WishList Member in the Downloads section of the Customer Center.
Note 1: It is recommended to back up your entire WordPress site before any upgrades or uploads. Having a complete copy of your site provides the option to roll back if you have any unexpected issues. This is a good idea whenever upgrading or uploading any plugins.
Note 2: Only For Those Who Use Extensions/Language Files. Extensions/Language Files may be deleted during an upgrade/upload based on how your FTP program handles the upgrade/upload process. Different FTP programs handle this differently. We recommend you backup your WordPress database including any existing extensions and any language directories (if you use different languages on your site) before you upgrade WishList Member.