Playback with screen off

Normally it works very well with screen off. Right now I just came back from a walk, listening all the time to ebook via Bluetooth headset, screen off. It may be that Android system on your device is set to kill apps in the background, or stop them, to save battery. Depending on the device you have and Android version, there are different ways of fixing it. Usually you need to go to Android system settings - Battery, find something like "Battery optimization" (on my Nexus 6P I need to press menu button at top right to find it) and add the app you want to keep working in the background or with screen off there. I could maybe tell more knowing which device exactly you have, and which version of Android.
 
Specifically I got a note from Huawei P9 Lite phone (probably applies to many other Huawei phones), that require additional steps to stop killing the app working in background:
 
You need to go into System settings – Advanced settings – Memory – Memory cleaning – Settings there (gear icon at top right) – turn off the “Automatic cleaning” option. He also says that he adds @Voice to the “white list of memory cleaning” as apps that we don’t want to be “memory cleaned”, but earlier he had @Voice added to that list and it did not help, had to turn off memory cleaning completely.