My PC finally broke and I built a new one. New hard drive, new Windows 10 installation from scratch. I installed AIS again, and the every few days this issue occurs. It in fact just happened again now. In Chrome I would see the "No Internet Connection" dinosaur, and nothing on my PC is able to connect to the Internet. I disable the Avast shields, and immediately my connection returns, upon which I turn the shields back on again and the connection is fine for a day or two.
This still happens to my wife's PC as well (as recent as yesterday morning), and yes, we are on the same LAN connection. Neither repair nor reinstall did anything to solve the issue.