WINS is looking for a Security Group in AD called "WINS Users". It needs this group for read-only authorization which means, users belonging to this group have read-only access to the WINS database. Now, documentation says, the group is created when WINS is installed. I found out it is not (for whatever reasons).
To fix this and make the error go away forever, just create a new Domain Level Security Group in AD called "WINS Users". It doesn't even need anyone attached to it. Problem solved. Restart the WINS service and you don't get that error any more.
According to a support forum, this error was recorded in a situation where the access to the Wins server was blocked by a firewall. Configuring the proper firewall rules (to allow Wins-related traffic) fixed the problem.