No matter what I did - changed the update options, reboot the appliance - didn't help. Looking on communities.vmware.com I found the post 477322 which presented the same behavior, only for vCenter Server Appliance and it was from 2014. So I tried (a bit skeptically) to start the update from CLI as suggested in the post:
- ssh to vRB appliance
- /opt/vmware/bin/vamicli update --check
- /opt/vmware/bin/vamicli --install latest --accepteula
And it worked:
I suppose this workaround can be applied to most of the appliances.