Why hasn't Team Rocket's Meowth evolved?
Meowth can't evolve because he can't battle.

As stated on Meowth's Bulbapedia article:


  Meowth normally does not battle unless there are extreme circumstances; his explanation is that his ability to talk and walk upright came at the expense of battling ability.


A good example of this is Pokémon: The First Movie, where Meowth and his clone are two of the only three Pokémon that don't get involved in the final battle (the third being Ash's Pikachu, who refuses to fight back against his clone). Because Meowth never fights, he never earns any experience, and therefore he can never evolve.

I guess Team Rocket could just stuff him full of Rare Candies until he evolves into Persian, but that then raises the question of where they would get all those Rare Candies from, as they're consistently shown to be short on funds.