Chess.com stores all of your games (Online Turn-based and Live) so you can download or access them at any time.
Premium Members have access to ALL games ever played on Chess.com. Basic members have access to all games played within the last 30 days. Once you subscribe, you will have access to all your old games once again!
Your online games history is beneath the current games list
http://www.chess.com/echess/profile/IisPro_
When you go to 'Play Live Now', before clicking on that button to enter live chess, if you scroll down it will show you your ratings and live chess games history there
http://www.chess.com/livechess/profile/IisPro_
Is there a games history for your account on this site? If there is, is it a gold/platinum/diamond feature? I'd be very nice to look over my past games. Thanks!!