Did you get your National Dex?
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You have to get the national dex then bebe will give you one eevee and you won't get another one so evolve it wisely.
You have to beat the Elite 4 to get the National Pokedex. Then you go to Bebe and she will give you an Eevee.
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After you get the National Dex
Talk to her after finishing the main storyline in the game.