Oh, you mean you set Autoplay for playlist A to on, then switched to playlist B and it did stop, right?
That's working as intended. The Playlist Autoplay setting only works within this playlist. If you select a song from another playlist to play next, it will not continue the playlist specific autoplay because you are switching to another playlist. Except playlist B has also Autoplay enabled.
So if you want autoplay in that case, turn it on for the song.