Avast! Free Antivirus - Program version: 11.2.2262 - Virus definition version: 160620-1
I am having the same problem with 2 Lenovo ThinkCentre PCs running Windows 7 Pro x64. Quick scans are scheduled every few days, with "Shut down the system after the scan finishes" checked in settings.. I watched one this evening; when the scan completed, it started the 60 second countdown. Once it reached Zero, the warning window disappeared, but no shutdown occurred.
I discovered this error has been occurring for well over a week. I'm not sure at this moment if these machines have clean installs of version 11.2.2262, or were updated from previous versions.
Upon further investigation, I will report back.
In the last hour I have "updated" a Windows 10 Home x64 machine from Avast! Free version 11.2.2262, to version 12.1.2272 (not Beta). I will know within the hour if this machine shuts down as planned.