Hmmm this is indeed tricky, you seem to have a healthy Joomla install. It's possible a script junkie may have done something cheeky in a comment, but lets not jump to that yet.
It may be a misconfigured .htaccess file, try using the Joomla default. Otherwise we might have a bug in the Latest Comments module, unfortunately I can't replicate the problem myself so I have no idea what else to suggest
EDIT: Is your webhost on a Shared hosting plan? Hows' the system resources in your cPanel? I.e. RAM/CPU usage and number of running processes?
EDIT2: Do you have the $livesite variable set in Joomla's global configuration?
EDIT3: Do you have the ZakAuthor plugin? Try disabling it if you do. Try disabling
all 3rd-party article plugins and see if it still happens.