Support

The problem is that Panopticon cannot access the API on your site. The fact that the version and PHP information tell you that the site doesn't report anything is telling us that.

Which version of Panopticon and the connector plugin are you using?

In your WordPress site go to Tools, Panopticon, and set Report System Information to No. Click on Save Settings.

Go to Panopticon and open the site's page. Click on the reload icon next to WordPress Update. Make sure you get the WordPress and PHP version back. Then click on the reload icon next to Extensions. Make sure "Admin Tools Professional for WordPress" is listed there.

That has made no difference

Do you mean that you still do not see the WordPress and PHP version?

Also, have you tried installing Admin Tools Professional again on that site?

The problem is that you are not getting the WordPress and PHP version information. Part of that API response tells Panopticon whether Admin Tools is installed, and a few of its basic settings:

 "admintools": {
   "enabled": true,
   "renamed": false,
   "secret_word": null,
   "admindir": "foobar",
   "awayschedule": {
     "timezone": "Europe\/Athens",
     "from": "",
     "to": ""
   }
 }

That's because WordPress does not have fixed names for its plugins, as opposed to Joomla having fixed names for its extensions. Therefore, we can not necessarily tell if Admin Tools is installed just by looking if a plugin named admintoolswp is installed. Admin Tools may be installed under a different name, or a different plugin may be installed under this name. Likewise, just because a plugin has a human-readable "Admin Tools Professional" doesn't mean it's necessarily Admin Tools. What the Panopticon plugin connector does is check for a unique constant defined by Admin Tools which tells us if Admin Tools Professional is really installed, and which name it's installed under.

Since this information is not communicated to Panopticon, Panopticon assumes that the plugin is not installed correctly or disabled. After all, we see a plugin called "Admin Tools" reported as installed, but there is no information from the API telling us that Admin Tools Professional is enabled.

I don't know why your site would only block the response from the /v1/panopticon/core/update endpoint but not anything else. That's why I had you check if the Panopticon connector is installed, and whether your site is configured correctly in Panopticon. These two conditions are met, therefore whatever you have must be some issue either with a their party plugin or your server blocking our connector plugin's response.