I can confirm, that so long as DS Audio (or my Bose SoundTouch) app is running in the background (they can be idle, they don't have to be doing anything like streaming music) I get live updates in the WeatherLink app.
If I forcefully terminate the app in background, no more live updates from Weatherlink - when I exit and re-enter my station display, it continues to work if I leave my station displayed without the other app in background.
At least I have a workaround for now!