|When the disconnect happens, does the server itself still have connectivity?|
Do you have more than two web servers you're hosting? If yes, is this problem only affecting two of them or all of them?
If you have more than two and the issue is only affecting two, then it seems most likely the problem is with the two and that's where I'd start troubleshooting myself.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.