Other users, including myself, have raised the same issue plus other related issues that impact knowing when an Internet connection is lost or the network is down:
This reply basically sums up the current situation:
So, if users really want this feature then you should let the GlassWire team know so it gets a high priority.
By the way, this is unlikely to be a small feature because there are so many reasons why the Internet connection can be lost. So GlassWire would have to diagnose the cause of the lost connection before it knows when to alert and what to alert.