Yes, I too have not resolved my issue, after all. I thought I had. My first statement at the top is still true. I have tested my Samsung phone and tablet with their native browsers and had no issue, yet. Another laptop in my home finally failed on the Chrome browser, as well.
Clearing the web browser cache does not fix the issue, no matter how many times I try. If I run CCleaner, it repairs the problem. I have not tested which operating system or browser setting is accomplishing this. After CCleaner, I can play the looped playlist, pause and start, advance the songs, and it all works.
I am not sure what triggers it to fail, but sometime later it will just stop automatically advancing. I can test if it has failed by playing the song and clicking the advance button. It will advance to the next song, but stop the device. I can hit play again and it works until it reaches the next song or I manually advance it.
I have completely shut off and cleared WP Super Cache. I am not sure if it triggered any of this, but I will test it out. I will look for which setting CCleaner is clearing.