Turns out this may be one of the WP 4.4 bugs that’s documented on WordPress.org’s support forums at https://wordpress.org/support/topic/read-this-first-wordpress-44-master-list
Plugins and Themes Won’t Update
An exceptionally small subset of users have reporting that after upgrading they cannot update plugins and themes. As of yet we have found no rhyme or reason for that to happen, but we are looking. If you’re having this issue, please provide as MUCH detail about your server as possible (OS, PHP version and flavor, etc). For now, you can “update” plugins and themes by deleting and installing the latest version. An official fix is in progress: https://core.trac.wordpress.org/ticket/34976
The problem with updating GP or GP Premium this way is that I have to export all my settings every time there’s an update.