The notification in settings is just a reminder and a shortcut for redeeming. It appearing or disappearing does not affect the offer per se. You can manually redeem in the app that corresponds to the service on the new qualifying device.
Current offers - Apple
- New subscribers get three months of Apple Fitness+ (where available) free when you buy a new eligible Apple Watch, iPhone, iPad, or Apple TV, subject to the terms and conditions herein.
- New and qualified returning subscribers get three months of Apple TV+ (where available) free when you buy a new iPhone, iPad, Apple TV, or Mac, subject to the terms and conditions herein.
- New and qualified returning subscribers get three months of Apple Arcade (where available) free when you buy an eligible new iPhone, iPad, Apple TV, or Mac, subject to the terms and conditions herein.
- New subscribers get three months of Apple Music (where available) free with eligible new iPhone, iPad, Apple TV, Apple Watch, Mac, AirPods, HomePod speakers, or Beats headphones, subject to the terms and conditions herein.
- New subscribers get three months of Apple News+ (where available) free when you buy a new iPhone, iPad, or Mac, subject to the terms and conditions herein.
The offers are for new subscribers that haven’t tried these services yet. That excludes past availability through Family Sharing as well.
The offers should be claimed within 90 days of activating the new qualifying Apple device with your own Apple Account. Gifting a device to someone else, shifts the offer to the first user of that new device.
The Apple Fitness+ offer should be redeemed in the Apple Fitness app on the new qualifying Apple device. The Apple TV+ offer should be redeemed in the Apple TV app on the new qualifying Apple device. The Apple Arcade offer should be redeemed in the App Store app on the new qualifying Apple device. The Apple Music offer should be redeemed in the Apple Music app on the iPhone or iPad to which the AirPods Pro are paired.
If you still need assistance after these considerations, then please contact the Apple Support staff.