Its happiness will stay the same even if you stop it from evolving.
Doing these things do not effect happiness. Source
- Depositing a Pokémon in the Pokémon Storage System
- Healing a Pokémon with low HP or with a status condition
- Giving a Pokémon an item to hold (except the Soothe Bell)
- Evolving a Pokémon, regardless of method (level up, held item, or evolutionary stone, with the exception of trade evolutions, which reset the Pokémon's friendship)
- Using a Pokémon in battles
- Winning battles with a Pokémon
- Letting a Pokémon's HP fall to critical status
- Letting the player's Pokémon get a status condition like paralysis
- Walking when the player's Pokémon has a status condition
- Affection in Pokémon-Amie
I hope this helped.