Unfortunately once you are disconnected from a game in the Live Chess there is no way to reconnect to it.
I would recommend that you try clearing your browser cache/temporary internet files (http://support.chess.com/index.php?_m=troubleshooter&_a=steps&troubleshootercatid=1&parentid=0) as this may help to correct any connection issues you are experiencing.
Also at http://www.chess.com/livechess you will find a notice at the top of the page which recommends a web browser which will give you the most stable connection to the Live Chess.
So I was about to win a game (like mate in a couple) and then the live chess gets disconnected and it was gone when I reconnected. I have had this happen many times but this time I started moving my mouse around and clicking on pieces and it still became disconnected. How do I fix this is really annoying