It does not appear to expire. It looks to be permanent, at least until Switch's online funcionality is retired.
Every Poké Ball Plus contains your very own Mythical Pokémon Mew, a special Pokémon that cannot be obtained by normal gameplay in any of the main Pokémon series games.
https://pokeballplus.nintendo.com/
Just remember although there doesn't seems to be a deadline, you can only redeem Mew once.
