Is it possible to re-battle gym leaders multiple times in the battle chateau in Pokémon X after defeating them?

Yes, it is possible according to Bulbapedia. It states:

In X and Y, the Gym Leaders of Kalos can be rematched at the Battle Chateau once the player has reached the rank of Marquis or Marchioness. The Gym Leaders use two of their Pokémon, who start at level 40. After the player has entered the Hall of Fame, the base level of their team is changed to level 50, and the Pokémon for some of the Gym Leaders have been replaced.

You can also rematch the Elite Four and the Champion at the Elite Four, but their levels will not change there. However, you can also encounter them at the Battle Chateau, as explained below.

Unlike in previous games, the Elite Four and Champion of Kalos do not receive higher level teams when rematched at the Pokémon League. Instead, they can also be encountered at the Chateau. The Elite Four can be rematched when the player reaches the rank of Duke or Duchess. They use three Pokémon at the base level of 55. Finally, Champion Diantha can be rematched when the player reaches the highest rank, Grand Duke or Grand Duchess, respectively. She uses four Pokémon, including her Mega Gardevoir, at the base level of 60.

You are also able to purchase writs to give certain effects that will also apply to the Gym Leaders, Elite Four members, and the Champion. The writs I would suggest to maximize money and experience would be as follows:

• Silver Writ of Invitation (100,000): A new Trainer appears six times as often (once every minute).
• Gold Writ of Invitation (100,000): Increases battle winnings by 50%.
• Black Writ of Challenge (300,000): Increases the levels of Pokémon by 20 (consequently increasing battle winnings).

Like other Trainers at the Battle Chateau, issuing certain writs can be used to adjust the levels of the teams used there by Gym Leaders, the Elite Four, and Diantha, as well as giving them the chance to appear more frequently.