The same thing keeps happening to me. I sync my 5s to my late 2013 MBP (15" Retina) and my playlists work for a while. Then, for some unknown reason, on several playlists some or all of the songs just disappear. They are still on the phone, but not in the playlists.
The temporary fix I have been using is to unsync all music from the phone and then resync all of my music to the phone. This takes a while, since I have over 20GB of music on the phone. I have done this twice and am doing it again now. If this doesn't stop the issue, I will try backing up the whole phone and then restoring to factory settings and setting it up again as I did when it was new. This never happened on my 4s. . .
One other strange thing that is happening--I duplicated one of the troubled playlists and gave it a different name. When I tried to unsync the other playlist and sync the new one, iTunes said I didn't have enough space (though I have 10GB free). So I unchecked "Sync Music" and clicked "Apply." It farted around for a while, but didn't ultimately clear out as much hard drive room on the phone as the music had occupied. So I synced the phone again with music unchecked, and it only then cleared all of my music off of the phone. Then I was able to recheck "Sync Music" and everything came back and worked, for a while. . .