Hello erdenefromnull,
Taking a look at, Download and stream shows and movies from Apple TV+ and Apple TV channels:
"You might have reached the limits for downloads, or the channel might not allow downloads.
- You can't download content from the Apple TV app on Apple TV, smart TVs, streaming devices, and on tv.apple.com. Instead, you stream content on these devices.
Limits for downloads
For most Apple TV channels, downloads are available for up to 30 days before they expire. For a few channels, downloads might expire earlier.
Some Apple TV channels might have limits for how many titles can be downloaded simultaneously and the number of devices you can download content on. If you reach the limit, the Apple TV app alerts you. If you want to download more titles, delete TV episodes or movies that you already downloaded from one of your (or your family's) devices."
Regards.