I have an application which takes measurements every second (I am running it in demo mode & generating random data, so the problem is not to do with reading from devices attached to the serial port).

After 5 or 6 minutes it hangs.

I have added

try
  // entire body of procedure/function goes here

except
     on E: Exception do
        begin
           MessageDlg('Internal coding error in <function name>()', 
                          mtError, [mbOK], 0);
        end;
end;

to every single function (and Application.Run() in the project file), but I don't see any message dialogs. Any idea how I can test this?