The first thing I would do, on the problem system, is set Robocopy to keep a log file (/LOG:{Path and filename}) and review this. Looking over a document I have, code 8 indicates "Some files or directories could not be copied." I think the word "some" is going to be the important one.
Maybe there's a "hidden" file or folder that your batch is failing to copy.
Although, I just re-read your post, saw that you are logging your copies and not seeing any errors.
Maybe try pointing both your SQL backup and batch file to a different folder on the server? I've seen some weird permissions issues in the past where everything looks good, but the user would still get errors.
Jason