Yeah, not asking for an auto reboot; that would be horrible. But the app isn't asking for a computer restart: it says application restart. And when I punch yes, it does indeed restart the application.
According to the Timeline feature of the application, it updated its a/v and other databases 6 times yesterday and I only had it on between 5pm and 11pm. Previous days this week ranged between 8 and 11 updates every day. At one point yesterday, I got the popup twice within 15 minutes.
It is definitely the case that the app icon in systray changes color during the application restart, and sometimes I have to manually re-enable protection after it is done. When that happens I can see entries in the event log where SecurityCenter is reporting "Updated Kaspersky status successfully to SECURITY_PRODUCT_STATE_SNOOZED." without a following "...SECURITY_PRODUCT_STATE_ON.", but I don't see any events reported for Kaspersky itself.
The computer is completely shut down daily, other than Saturday nights when it performs scheduled backups.