I get the same issue and I am wondering if it is because I have the 'repeat' setting enabled.
My playlist has several hundred tracks but when I tap 'Shuffle play' or on any track and look at the queue only a smaller sample of the playlist is in the queue. When the player gets to the end of the queue what should happen is that the queue is refreshed with a bunch of new tracks from the playlist. I'm wondering by having 'repeat' enabled the player is simply repeating the queue and not refreshing.
Personally I've never liked the queuing system in Spotify. It is fungly and unpredictable at the best of times..
This happens to me but only in the web version of Spotify. It seems to be a buffer problem but I have noticed that for a while and there are no Spotify remedies or updates. A playlist as an example of more than 100 songs, when it reaches 25 it freezes. It seems to happen in the PC application but I have no problems there, only in the Spotify Web Player.