The mms.cfg file appears to be configured correctly. Are you deploying the mms.cfg file before or after deploying the installer? What version of Flash Player is being installed on the system? Can you provide the entire log file for an impacted system? The log file will most likely be fairly large, The forums don't accept attachments. You can upload the log file to cloud.acrobat.com using the instructions The specified item was not found. or some other file sharing software and then private message me the URL to the uploaded log files.
I think when we migrated the server hosting background updates (from Server 2008 to Server 2012 R2), we must have neglected to configure SSL/certificates for the background updates site in IIS. I had corrected that before starting this discussion, but for some reason, manually running the Flash updater scheduled task (for testing) wasn't working properly. But yesterday (11/3), when I checked IIS logs, I noticed entries for the Flash updater. When I checked a system where manually running the scheduled task had failed previously, Flash was updated. So this seems to be working now...