I can’t provide any insight into the issue I’m afraid, but those that can will probably want to know what version of the app you are running, and what version of local server as well.
Information from the Blynk local server logs, especially those relating to the notification send process will probably be helpful too.
I assume that your local server has a constant connection to the internet and that there are no issues with this, and that you’ve tried rebooting everything, including the router?
There was an issue previously with iOS notifications, which required the Blynk app to be uninstalled then reinstalled to fix the issue…
Pete.