If you are away from your computer for a while and lose connection to the Trello servers because your computer went to sleep, or you temporarily lose your network connection, an information box will appear in the bottom left hand corner of the browser notifying you that you have been disconnected from the Trello server.
One thing that can definitely increase the risk of the connection being lost is keeping a browser window open with Trello for long periods of time. Making sure to refresh the page periodically, especially after waking the computer from sleep, will help make sure that stays active.
While you are disconnected from the Trello servers any edits that you make to your Trello cards will not be synced or saved to your boards. When you see this red warning box, check your network connection, and once it has been restored reload Trello before making any edits to your cards.