I've been having a similar issue. My issue seems to stem from music that I ripped ages ago and imported to my phone. I will add it to a playlist that has Apple Music songs and the songs will be added until I click them to play and then disappear. Haven't been able to find a fix
Had the same problem today. All of a sudden adding a song to a playlist didn't work. Workaround was to add the song to my music, remove from my music and then add to playlist again. I also reported this bug to Apple.