This quest will expire after the events at the Mechonis Core.
Getting a Member's Card is a Timed Surprise Quest in Xenoblade Chronicles. It is automatically triggered in Alcamoth during the course of Destroying the City Trade, that is received from Gadada in Frontier Village.
Notes
If the party enters the Secret Club without the Club Card, they will be kicked out by the High Entia bouncer.
After the completion of this quest, since Dedeba has been arrested, it will be impossible to meet him again until the end of the game.