Apple TV, unable to download rented movies, can only download purchased ones

Did you check the amount of free space on the iPad? You seem to have a pretty new model, so ‘disk full’ shouldn’t be an issue so soon, unless you download a lot to it. How to check the storage on your iPhone, iPad, and iPod touch - Apple Support

Rented content can be downloaded to one device at a time. If downloaded elsewhere, then it wouldn’t be downloadable on iPad. Downloads will be automatically removed after the rental period.

Rent movies from the Apple TV app - Apple Support

If the issue persists despite the above, then I would suggest to contact an expert from the Apple Support staff for further assistance. Contact Apple for support and service (phone numbers) or start your support request online (chat/​email/​callback).

I am also having this same issue. I have been working with Apple support for over a month now. I have done everything Apple has me do, with them logged into my Ipad to see the error messages and nothing works.

Have you been able to resolve your issue? If yes, how?? Apple doesn't seem to have the solution for me and so far has not been willing to authorize a replacement, rendering my purchase to boat anchor status.