I am having exactly the same issue and also for me "everything used to work fine". It's only been in the past 2 weeks when I deleted a bunch of songs that now my songs won't play, or the next song in the playlist plays while still showing the former song, or entire albums just don't play at all.
It seems like is started for me when I unchecked "show all music library" in my Music Settings so I would only see the music that I had downloaded to my phone. But I have tried "show all music" again and turning off and on iTunes Match but nothing seems to help.
This is a real problem...hopefully Apple can get this one fixed or someone has a solution...