In the Live Agent Chat, the notifications pop-up on your screen and then quickly fade from view within a few seconds.
If you are not looking at your screen during those few seconds, you miss the chat!
This is assuming that you have the over loud, same for everyone, "alarm" sound turned off. Also that you do not have the Service Cloud tab with the Live Agent chat on it as your front screen. Two things that happen all of the time in an office.
I'd like the Notification to stay on screen, until the Chat is picked up.