The setting that controls this is:
Settings﹥Apps﹥TV app﹥Use Play History﹥On|Off
It should be set to ‘On’ for what you want from it, which would be the default setting.
If it is still misbehaving with this setting on, then
- Force-quit the app, then relaunch and try again.
- If the issue persists, force-quit the app, restart the device, then relaunch and try again.
- If the issue still persists after that, then contact Apple Support for further assistance.
As the Apple TV box is potentially a multi-user device, also verify that the intended account is set to be the active account. Else you could be changing someone else’s watch progress instead of your own. Switch the active user profile on Apple TV - Apple Support
I’ve logged out and back in, but no change.
That is a good troubleshooting step for this, but may not be enough in this particular case, unfortunately.