Time Machine "Back up automatically" does not stay ON - Mac OS High Sierra

Time Machine: The "Back up automatically" tick box does not stay on. When I click it, it stays on for a second, then goes to unchecked state, and there are no automatic backups taking place.

I can still run backups manually, and TM shows my previous backups all right. The backup disk is directly connected to one of the Thuderbolt ports, and the disk has enough space and is formatted for MAC OS extended, journaled.

The problem started already with the previous OS version, and updating to High Sierra did not help.

MacBook Pro 15", mid-2014

MacOS High Sierra 10.13.6