I’ve looked at similar threads but couldn’t find a solution.
Running latest version of Blynk (2.27.12) on Android 4.4.2.
Using https://github.com/vshymanskyy/blynk-library-python/ on Pi 3 via ethernet.
Notification setting “Priority” is High.
“Notify when hardware goes offline” set to Off. (Also tried on and 1 sec, but made no difference.)
No other Blynk apps are using this auth token connection.
Notification works fine every time so long as Blynk is running as present app on phone, but the notification doesn’t work if it’s running in the background or if screen turned off or if in open app menu.
Also an idea: it would be good to be able to have more than 1 notification for the sake of different noises eg. so I can hear a certain noise from my phone when event A happens, and a different noise when event B happens, warranting each notification their own virtual pin I suppose. This would be lovely 
Thanks