I did another test today.
I booted the PC. After 11 hours of uptime I ran the Smart Scan. It ran, and failed. Of course. Sigh.
Then, an hour later, at 12 hours and 10 seconds of uptime: like clockwork .. the Smart Scan results window popped up again out of nowhere.
So somewhere in the code of Avast is a bug related to 12 hours uptime and the Smart Scan.