I double checked, and the app is actually trying to continue download after you navigate away from it, or turn off the screen. However what I forgot to do was to set a "wake lock", to tell Android system to keep the app running, do not stop it when it's in the background. I added wake locks now, the change will be in version 22.4.10 or any newer. Even now though, you could try to press e.g. the Home button while a long sync works, and then pull down notifications - you'll see the text flashing in the @Voice notification telling that it downloads subsequent articles, and in the end they do get added to the list. Unless the system stops the app...
It may still happen on many devices, where the manufacturers modify Android system to kill or put to sleep apps that run in the background or with the screen off, to "save battery". The most often complaint and symptom of this is when you try to listen to a long text with screen off - many devices will then kill @Voice process or stop it, and speech stops. The same problem could occur here with a sync running in the background or with the screen off. If you or anyone else runs into this problem, please visit https://dontkillmyapp.com
web site, press there on the device type you have, read and implement the settings recommended there.