The reason is probably the default double click behavior. You never actualy play things directly from playlists in MC, you select songs to move to Playing Now. If you enter Playing Now you will see that the list consists of only one song. That is why it stops after each one.
You need to go to Options, General and Bahavior. There you have the Double-click option. I always use the "Add as next to play". That way you never wipe the Playing now clean. You can also select Replace Playing Now (all), if you prefer to add whole playlists and clear playing now every time.