Are you using the xbox music app? Go to the now playing page, then next to the shuffle icon there's a symbol that looks a bit like a "u". Hit that once to keep the playlist on repeat, and twice to keep the song on repeat (should now show the"u" with a little 1 next to it.
In the music app, next to the song that's currently playing, you'll see a mostly completed circle with an arrow pointing clock wise. Press it once to repeat the album/artist/playlist you're listening to. It should turn from greyed out white when you do this.
Press that icon again and a "1" should appear on it. That indicates the song currently playing will repeat itself until you either turn repeat off or until you close the app completely.