Hi there David Dalzell,
If the Apple TV app is prompting you to sign into your Apple ID every time you open it, the first thing we would recommend is to ensure the app is fully updated. This installs feature improvements and bug fixes that can resolve unexpected behavior like this. This information from If you can't watch or stream movies and TV shows in the Apple TV app shows how to check this:
If you're using a compatible smart TV, streaming device, or gaming console that's connected to the internet, the Apple TV app should update automatically. If you need help, you can contact the manufacturer or learn how to get the Apple TV app on your device.
The 'If the movie or TV show won't start playing' section of that article has some other troubleshooting steps that can help with this issue as well.
If something else is occurring, please provide more details so that we can continue to assist.
Cheers!