Maybe try clearing the cache and uninstalling the Roku mobile app from your phone. Then Restart the phone and Reinstall the Roku mobile app.
I use the mobile app on an Android Moto Z with Android v7.1.1 and I am able to minimize (swipe close) the app and the private listening will continue. (both with wired and bluetooth headphones/earbuds).
There is a possibility there may be a bug in the app with either your particular phone or the Android version, though, so can't rule that out.
Normally, if I run into the intermittent issue with the mobile app, a clean install will remedy it. (I will usually clear all data and storage cache and do the phone restart before reinstalling).
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