Not that I know for sure, but I doubt it has anything to do with the app, other than it being the recipient of the push notification. I expect the server monitors the system, and sends a push notification to the app, when it spots any issue, including any offline status. As such, it could easily be your router.
Indeed, I tested my system by turning off my router, and got the same message to my phone. After I gave my PC internet access, using my phone’s hot spot for the test, on checking the Blink app, on an emulation of my phone on my PC, where the app hadn’t even been running, until I loaded it, and not until after my real phone had already notified me. The push notification arrived there too, so that app couldn’t have been monitoring anything, so in my opinion it must be a function of the server.
If it always goes off at 3AM, set your alarm for 3AM, and test your internet access with other devices. If you have none, then you can check your router for settings, or call your ISP, to see if any limitations have been applied. If you don’t want to get up at 3AM ask your ISP to check it for you anyway.