System status blank - error message changing resource url
The system status page uses ajax requests. Browsers won't let ajax requests access data on a server that has a different hostname from the one where the request started.

So your second install can be accessed by a different domain but thinks it has another name. You can check this in your browser's developer tools -> network tab to see what url the system status page is trying to access.

For example you are visiting my2ndsite.org but the system status page is trying to access someOtherName.org.

If you state which http server (e.g. apache) and which CMS (e.g. drupal) and maybe some details about your virtual host config it would help give a more specific answer.