What app are you using to play the music? Maybe it’s a feature of the app? Like, if it’s for streaming music, many music streaming services have an idle timeout where they will stop playing because they don’t want to pay royalties for playing music to an empty room.
I am using the Amazon Music app on the latest version of the Fire stick.I have them on two televisions and the stoppage happens on both of them. Music plays all day on other apps but I want to use Amazon Music app. Any help is appreciated.