API Key Failure

We recently attempted to install Wordfence to run some scans. However, when we installed it, it seems that it failed to get an API key; we have this message on our dashboard:

Wordfence could not get an API key from the Wordfence scanning servers when it activated. You can try to fix this by going to the Wordfence “options” page and hitting “Save Changes”. This will cause Wordfence to retry fetching an API key for you. If you keep seeing this error it usually means your WordPress server can’t connect to our scanning servers. You can try asking your WordPress host to allow your WordPress server to connect to noc1.wordfence.com.
We tried saving the options page as suggested, but no matter what it fails to save any options or retrieve the API key. When we try to save, we get this message:

Please reload this page

You selected a config option that requires a page reload. Click the button below to reload this page to update the menu.
And nothing saves on reload. Oddly, the Wordfence connectivity tester passes:

Wordfence connectivity tester

DNS lookup for noc1.wordfence.com returns: 69.46.36.8

STARTING CURL http CONNECTION TEST….
Curl connectivity test passed.

STARTING CURL https CONNECTION TEST….
Curl connectivity test passed.

Starting wp_remote_post() test
wp_remote_post() test to noc1.wordfence.com passed!

Starting wp_remote_post() test
wp_remote_post() test to noc1.wordfence.com passed!
The server memory test also passes.

The “you just installed Wordfence” tour dialog box also shows up every time any page in the dashboard is loaded and must be dismissed again. Uninstalling and re-installing the plugin has no effect either (and since we can’t save options, it’s also not possible to check the “Delete Wordfence tables and data on deactivation?” option).

https://wordpress.org/plugins/wordfence/