We haven't received a lot of new reports of this issue, so the reason of this behavior is more likely device or account related.
That would be weird, because the account works fine on e.g. phones or whatever, and the Xbox works fine with ... well, absolutely everything else 🙂 I mean, I get that tracking these things down can be hard, but it's difficult to reconcile "problem at your end" with all the other things working great.
I initially thought it might be something to do with Spotify's handoff between phone and Xbox, but the problem persists if I use the XBox to play a playlist without using the phone. Sometimes it's five songs, sometimes ten, but it will always fail to keep playing at a random point (most often, but not limited to, the start of a track).
One thing you can still try is to check if Xbox comes up under the list of third party apps that have access to Spotify. If that's the case, remove this access and let us know if that makes a difference. You can learn how to do this here.
Thanks for the suggestion. The Xbox doesn't appear there (only the PlayStation) and to the best of my recollection hasn't ever.
I can't find many settings within the Spotify Xbox app itself - are there other things I could try?