About a week or so ago, a member posted a thread at Search Engine Watch Forums named Significant flaw in desktop search - Outlook which describes how Yahoo Desktop Search locks your mail file (.PST), preventing it from being backed up. So he asked in the thread if anyone knew a way around it. So I emailed Yahoo! and they provided an answer.
There are actually very few steps for you to execute. Assuming that you'll be running a batch file to execute the backup:
1) Add a line to the batch file, prior to running the backup
c:\> taskkill.exe /f /im "YahooDesktopSearch.exe"
2) Add another line in the batch (after the backup is executed) to restart YDS.
c:\Program Files\Yahoo!\Yahoo! Desktop Search\> YahooDesktopSearch.exe
(Note: the path above may be slightly different on your computer, though this is the default path)
If this is done correctly, every time his backup is run, YDS will be shut down before and restarted after the backup is complete.
Forum discussion at Search Engine Watch Forums.