I'm having the same exact issues with Avast Home 4.8.1169. It shows the following:
Last scanned:
Last infected:
Scanned count: 0
Infected count: 0
Task Name: Resident protection
Run time: 2:53:24
I hear others saying that its OK, its working as it should and will pop up when it detects an attack. I'm not satisfied with that statement, because I had the Web Shield doing this same thing until I found, by luck, instructions on how to set up a proxy in Firefox.
So before I actually entered the required settings for Web Shield, it too was showing the same stats as Network Shield is now, and at the time, I thought Web Shield too was working as it should, but it obviously it wasn't.
Can you guys see my reason for concern?