Yes, it does stop playing. That's due to me ending the play status though.
I should maybe get me a portable-internet-headset-radio-podcast-device ...
As when I clean the bathroom, or take a powered walk, I tend to be too far away from the audio of the pc to still be able to follow the cast.
I am an old git. I do love my FM radio, would probably still do AM if I still had a device capable of receiving it...
(No, I am lying here, I do have DAB+ radio... )