Apple Music adds music to playlist which isn't really added to the list I currently using Apple Music since it's release and I encountered a strange problem. The first times I just thought that I've made something wrong. But now I tested it many times and won't work as expected.

I've had a song, which I wanted to be added to a playlist on my iPhone while listening to a self defined radio station. The song before that song could be added to my playlist (clicking ... > add to playlist > choose playlist). I rechecked it and it's added to my playlist without any error. The iPhone stated that the song is successfully added to my list.

The next song, I tried the same thing. I tried to add it, my iPhone stated again "added successfully". After that, I went to the playlist to check it, and it's not there. I go back to the song and tried to add it again, again successfully but no song in the list. I tried it even on different lists and no list work! 
I tried another song and it is added successfully again and... it is really added to the playlist. Just this one song (which is normally available in the store) can't be added to my playlist. 

Is there a limit which songs can be added per day? Is this an bug? Can some songs just be streamed but not added to a playlist (I don't talk about offline availability)?

Thanks in advance for your help. I don't have any clue whats going on there.
Well I just tested the other way round. Sorry I don't came on this on my own as I posted the question. 

I edited the playlist instead, search the currently playing song, added it and saved the playlist. This worked for me. But during the save process the iPhone really stutters heavy. It nearly freeze for a few seconds. This can be caused by the temperature currently in Germany (38 degree) but it's still strange.

Anyway, it should still work the other way around. But if someone else encounters a behavior which is quite the same, he can try to solve it like I did.