So... Apparently one of the recent Unitrends updates (7.1.0-5, specifically) broke my SharePoint backups. I'm not writing as much for assistance as I am to express my irritation at this. In my research, I found *no* release notes or customer bulletins anywhere that advised customers of this change (or that they would need to reconfigure their backups).
I figured out that it broke because my backups have been failing for the last week or so. I researched and found Unitrends changed the way the SharePoint backup credentials are used to run the job, but my research suggests this probably should have "broken" when we upgraded from version 7.0 to version 7.1. Per the documents posted at each of the below support articles...
Configuring SharePoint for backup with Unitrends 7.0 Application Backup http://support.unitrends.com/ikm/questions.php?questionid=851
Configuring SharePoint for backup with Unitrends 7.1 Application Backuphttp://support.unitrends.com/ikm/questions.php?questionid=952
The biggest difference between the two is that 7.0 has you run the Unitrends BP Agent service as the newly-created SharePoint Farm Backup account, whereas 7.1 has this service set as Local System, *then* the Farm credentials are set in the SharePoint server's backup configuration area of the Unitrends Recovery Console.
The 7.1 guide also has you add the backup account to the local administrators group on each server, which is unnecessary for customers coming from version 7.0. In 7.0, the farm backup account was added to Domain Admins, which is already a local admin on every server... Are they assuming no customers were using SharePoint backups on version 7.0? Or that those customers wouldn't upgrade to 7.1??
I've reset my agents to run as "Local System" and added the Farm credentials in the Recovery Console, so I'll have to wait and see if the backups complete successfully tonight.