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Sorry, but the other answer is incorrect.
This is on Pokémon Bank’s FAQ Page:
Question:
What happens to my Pokémon if the no-charge trial period ends or my paid pass expires when my Pokémon are still deposited in Pokémon Bank? Will my Pokémon be lost?
Answer:
If your trial pass or annual pass expires and you do not purchase a new pass, you can still withdraw your Pokémon from Pokémon Bank for a set period of time.However, once that set period of time ends, any Pokémon remaining in your Pokémon Bank Boxes will be lost [permanently].Be sure to withdraw your deposited Pokémon as soon as possible, or purchase a new annual pass.
Source.