Pokémon GO developer Niantic has confirmed that Pokémon GO Plus users are experiencing issues with App devices upgraded to iOS 11. The developer is currently investigating this and has released the following statement regarding the matter:
We are aware of an issue with the Pokémon GO Plus on Apple devices upgraded to iOS 11. As a result of this issue, the Pokémon GO Plus accessory does not register a button press until after the LED indicator light has flashed three times. We are working to resolve this problem.
Source: Pokémon GO support page