This should work, but I would probably handle it differently.  It just sends a query to a page on your server every 15 seconds.  If the query fails, then it is probably offline (either you or the server).
function checkOnline(){
    $.ajax({
        url: "test.php",
    }).done(function( html ) {
        if(html=='ok')
            setTimeout('checkOnline()',15000);
        else
            alert('Error');
    }).fail(function(){
        alert('Offline');
    });
}
test.php
<?php exit('ok'); ?>
I would personally attach a fail function to my other Ajax or polling queries.  If those failed, I would trigger the Offline message and cease further polling or queries until the page was reloaded or after a certain time interval.  No sense in just polling the server for the heck of it.