I have had this problem since the start (4 months ago) with Nokia Lumia 920. When I start music on the Nokia Music application, the first track goes normally smoothly, but the player stops to the beginning (0:00) of the second track. The playback button feezes to "II" i.e. "pause" button, and pressing it on and off again does not start the playback again any more without closing the Music application. This does not occur every time, but about 90% of the times I try to listen to music: both my own and mix radio.
Which verison of Nokia music are you using?
Make sure to use the latest version. You can upgrade Nokia music from the Store.
This might relate to Bluetooth controls. I listen to music using my Nokia BH-221 headset, as I find cables unconventional (but like to have a FM receiver). If I do not use Bluetooth, the music playback seems to work fine.
Could the problem be that the play/pause etc. controls available at the headset interfere with Nokia Music on Lumia phones?
I have had the same issue first with my 822 and now with the 928. It happens when using bluetooth in my car while playing offline mixes. It does not happen when I use a wired headset.