Acronis Backup 12.5: attempt to create or apply backup plan finishes with "Failed to connect to 127.0.0.1 port 30667: Connection refused"

Symptoms

1. You installed Acronis Backup 12.5 Update 4 (build 12730 and higher),
2. When you try to create a new backup plan or apply existing plan to a device, operation fails with the following error message

 Failed to connect to 127.0.0.1 port 30667: Connection refused