This same problem has been bedeviling me for months. I have a Roku Express and an Apple TV+ subscription, and watched all of "The Morning Show" without any problems. But I ran into issues trying to watch past the 2nd episode of Defending Jacob.
I tried many of the suggestions in the (currently) 9 pages of replies to this post, but most of them didn't work for me. Here's what did work.
Go to the Apple TV+ app on your Roku, and go to Settings
- turn on "Share Apple TV Analytics"
- turn on "Location"
*** I don't actually know if these 2 steps are required, but I don't want to omit them if they're in fact necessary
Start a show (e.g., Defending Jacob episode 3) on your iPhone, and *HERE'S THE REALLY IMPORTANT PART* let it play all the way through the highlights from prior episodes *AND* the credits; pause a few seconds after the new episode actually starts
- leave that episode open in the app on your iPhone
Go to the Apple TV+ app on your Roku, and click on the (paused) episode in "Up Next"
- others have said you need to delete the show from "Up Next", but I didn't have to do that
Editorial comment: I've noticed recently that content providers seem to be providing the intro/opening credits sequence in some kind of video format that's not always compatible with all streaming devices (e.g., 4K rather than 1080p?); for instance, I've had shows (on my Fire TV) that provide the audio but no video during the intro sequence, and only start showing video after the new episode actually starts. So this might actually be 2 problems that compound each other: (1) content providers that are creating videos that non-4K devices can't always properly interpret; and (2) device manufacturers that "puke" when they get content from #1, rather than handling it gracefully (at least my Fire TV just blacks out the video until the episode starts, rather than telling me that the whole episode simply "isn't available"). Assuming my conjecture is correct, the above instructions probably work because take you past the point in the video stream where the "problem" portions are...