I wonder if it would be possible for a sort of hidden "diagnostics" system automation task to run that could generate a link to a test URL, execute a CURL command against it to see if it receives the anticipated response. If it does, great! If it doesn't, there is an issue.. log the issue, and possibly send out a notification or display the issue in the "System Status" widget.
In the future, the "diagnostics" automation task could check for other issues as well.