It seems like the server is not responding to an AJAX request. I couldn’t reproduce the problem on that test page but if it’s intermittent maybe I just didn’t catch it.
I suggest checking both the PHP server logs and Apache logs. They should provide a clue about why the server isn’t answering. Unless it’s a connectivity problem, the only thing I can think of is an out of memory error (which would be in the PHP/Apache logs).
To test for a connectivity issue, you can just call admin-ajax.php directly – if you don’t see “0” output then the server didn’t respond: