Just to confirm :-) At the "Now playing" screen, do you have repeat mode (button left bottom) enabled? Is it green and does it display a 1 too, or is it just marked green? If so, tap it twice so that it will be marked as green so it will be at normal repeat mode.
I've been having the same problem for a few months, and it's not the repeat button. I have this problem on my iPhone as well as desktop. Any given station will only play about 10 different songs. They are always in the same order. I have reinstalled on both devices and the problem has not been fixed. Thumbs downing songs also does not work: the same song will show right back up. I am forced to use Pandora now if I want to listen to the radio.
I am having the same problem with radio. I'll listen to a station for approx half an hour then the station will repeat the last 3-4 songs continuously, skipping them does not help, it's quite frustrating.
It's happening with both playlists and radio -- I don't have repeat on. I've noticed that the queue has a number of unique songs listed but will periodically (actually, fairly frequently) reshuffle the same songs toward the top.
I can skip, skip, skip... to a new song -- but that's an annoying work-around.