We are having the same issues and began when we upgraded from 10.4.1 to 10.6.1. Source data FGDB and related dynamic map services are refreshed weekly (also not cache). For us, this is an intermittent issue as we have re-published other long running services and published new services without issue.
We publish from ArcMap 10.6.1 Client.
For those that re-publish with errors we get;
'Failed to rename cache folder error'
Then
'Geodatabase Error: General Function Failure'
Restarting the ArcGIS Windows services seems to flush out whatever was causing the issue.