Here's the cmdline I ran since your reply but I can't get it working:
RUNAS /user:<ourdomain>\<myuseracct> C:\Windows\System32\Robocopy.exe c:\Backup\ \\<servername>\<repositorypath>\ /E /z /MOV /NP >> .\ROBCOPY_LOG.TXT
I now seriously think this is actually a bug within ROBOCOPY because RUNAS works fine with notepad, etc (RUNAS /user:<ourdomain>\<myuseracct>) but does nothing with ROBOCOPY. Nothing is written to the logging file .\ROBCOPY_LOG.txt either - litterally nothing (blank file). It seems to exhibit the same behaviour as the SQL Agent job (basically does nothing). Maybe because SQL Agent is using RUNAS in the background it's encountering this same bug in ROBOCOPY. Can't see any other explanation.
Has anybody else used ROBOCOPY with RUNAS or as a SQL Agent EXECCmd?