There is a bug in iCloud Private Relay that causes some audio streams to stop playing in the background after a few minutes. This bug started happening with the iOS 16.6 release and continues in iOS 17.
 

We cannot workaround this issue and it's been reported to Apple who is actively investigating the problem.
 

Until this bug in iOS and iPadOS is fixed, you can turn off iCloud Private Relay in System Settings:
 

Apple ID > iCloud > Private Relay > OFF
 

We value our privacy on the Internet as much as you do, so we don't like making this recommendation. We're all hoping for a quick fix from Apple.