PokéBase - Pokémon Q&A
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It depends on when you battle them for the second time.
Levels never increase: RBY, GSC, RSE, DP, XY
Levels only increase after a certain in-game event: FRLG, Pt, HGSS
Levels increase upon second challenge: BWBW2, ORAS, SM, USM
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The events in question being the Stark Mountain post-game, Sevii post-game, and defeating Blue?
I think so.