Set Customer Time-Out in your associated Live Agent chat button. Specify a time period and when to send a warning to the visitor. For example, you can have the chat time out after 2 minutes, but send the visitor a notification after 90 seconds. The warning has a countdown, so the visitor knows exactly when the chat times out.
If the chat times out, visitors can see what happened in the chat window, so they don’t think their agent left without saying goodbye!