If I move the file to a personal folder on my Desktop PC, it won't delete from my BlackBerry.
Personal folders are not online and therefore will not sync to BlackBerry. If you move an email to a PST it will just sit on the BlackBerry as the BES won't know where the emails have gone.
Also check you reconciliation settings on the device:
Delete On: Mailbox and Handheld
The above setting will be in Messages - Options - Email Reconciliation
Lastly, sack your BESAdmin for being crap.