Yes, but they have to want the rematch. your pokenav has a feature called match call that lets you know when a trainer wants a rematch. There will be a box with a pokeball design on it next to the name of the trainer (or gym leader).
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You cannot rebattle Gym Leaders.
you cant
Touch a man...
...you beat the gym leaders
after you beat 4 to 5 gym leaders you can face him