I have the same problem. Well, at least somewhat. When my app is closed (not in background, completely closed), it is only awakened for roughly half of the started live activities.
I can't find any pattern in circumstances for when it fails:
It is not consistent wrt. devices
It is not consistent wrt. time-of-day
It is not consistent wrt. users
It is not consistent wrt. device connectivity
....?
I am pretty confident that the app is simply not granted any execution time.
When it DEOS work, I see that
application(_, didFinishLaunchingWithOptions)
happens, and 3-4 seconds after that, the activity-specific push-token comes in.