I have done some other tests:
1) if a phone has the screen off and I try to reach it, I receive the warning: "Device unreachable" or "Unable to get the location".
2) If I activate the screen on the phone, everything works immediately.
The app can be run in the background and runs automatically on startup in both phones.
The two phones have the same settings and both have the Prey shield in the left corner of the status bar; in addition, "Prey - protected" appears when I reactivate the screen