It isn't explicitly stated in the book or the film as far as I recall.
If your avatar dies in the game, you lose your possessions and your XP and have to start from fresh again from level 1, owning nothing. You could assume that a key would be the same.
Daito lost his position in the book when he was killed, but he was killed in real life. I can't see any indication of an Avatar being killed and seeing this reflected on the scoreboard.
However, you don't lose your own personal experience/knowledge. If you did lose your key(s), then you'd still remember how to get them and and catching up again won't take too long.