Michael said:
Maybe I misunderstand the problem, but what about simply copying the
.PST file to the desired location?
Which includes just about any backup program as long as it can read
and copy a file that is currently open in case Outlook is still loaded
(so one that can implement VSS backups should work). Even Microsoft
has their own PFB (Personal Folders Backup) utility that runs as an
add-on in Outlook so when you exit Outlook (after the number of days
specified) then it will save a copy of the .pst file.
MS PFB download page
http://www.microsoft.com/en-us/download/details.aspx?id=9003
Doesn't list OL2010 or OL2013 but then neither did the OP specify
which version of Outlook he/she is using. This only runs (after the
number of specified days) when exiting Outlook to ensure the .pst file
is closed. Because it runs after Outlook closes the .pst file, it
will make Outlook take longer to unload (as long as it takes to copy
the .pst file).