Hi there KeithAMoore,
If the issue seems to be happening outside of the country from where the movie was rented, it may be related to an issue with regional availability of that media or of the Apple TV app. 
The Apple TV app isn't available in all countries or regions. Click here to find out if the Apple TV app is available in that country or region: Availability of Apple Media Services - Apple Support. The Apple TV app and Apple TV+ app features and supported devices also might vary by country and region. Check out this link to learn more about renting and watching movies from the Apple TV app: Rent movies from the Apple TV app - Apple Support. 
Also, when downloading the movie for offline watching, did you download the movie while in the country from where it was rented, or in another country/region while traveling? This may also impact the availability of the movie being able to download to your device. 
If you downloaded in the same country where rented and you have an issue while also trying to play the movie in that same country/region, you may want to reach out to Apple Support directly so they can further assist. You can reach out to them by clicking here: Contact - Official Apple Support or over the phone by calling the number that is most local to your region: Contact Apple for support and service - Apple Support.
We hope this information helps you out. 
Best wishes!