I don't know if anyone else has seen this, but I wanted to post this here in case someone else runs into this issue.
(Edit: Enterprise 11.1.0)
This is in a multi-machine deployment with separate machines for Portal, Server, Imagery Server, the data store, and other registered data sources etc.
We run a batch process every night to take a new backup using the WEBGISDR tools. Recently we changed both our PortalAdmin and ServerAdmin for security reasons, and we made them different passwords. In the past they were the same. We changed the password in the WEBGISDR tool, but then it quit taking a backup for the ArcGIS Server. The other components worked, but not the ArcGIS Server. Way too much trouble shooting later, we changed the ServerAdming password to match the PortalAdmin and the WEBGISDR tool worked successfully again.
I scanned through the batch properties and tool properties and could not find anything detailing why or if there was a place to insert separate passwords etc. All I know is it works now.
I hope this helps someone else if they run into the same problem with a multi machine deployment.