YouTube paid memberships & device limits
You can use the offline features of YouTube Premium or YouTube Music Premium on up to 10 mobile devices at a time. Once you’ve reached this limit, if you try to download a video on a new device, the oldest of the 10 devices you've used previously will be de-authorized. You can do this up to four times in one year.
After you’ve made your fourth swap, you will see the message "Sorry, this video can't be taken offline." This means you’ve hit the limit on the number of devices you can use to download and you won’t be able to download videos on any new mobile devices. However, you can continue to use YouTube Red to download videos on any device you've used previously.
Note: You can also view and manage your devices in your Google Play Music account settings.