This happened to me too, running Windows 7 on a new computer. Approved Workman worked fine when I installed the demo version, but when I copied my church's master database over to my computer I got this error message.
I eventually figured out what was happening. When I ran the copy of ApprovedWorkman.exe from my USB stick, I got a popup window saying "Your temp directory is C:\WINDOWS\TEMP" plus some other text I don't remember. I didn't think anything of it at the time. But when I searched the forum, I discovered that the "Access denied to table or back up file #####" error usually has to do with temp files, and I thought, "Hmm, Windows 7 has some restrictive permissions by default."
So I tried to look at the C:\WINDOWS\TEMP folder on my hard disk, and Windows popped up a message box. "You currently do not have permissions to access this folder. To PERMANENTLY give yourself permission to access this folder, click this button." I clicked the button, made no other changes, and suddenly Approved Workman was working just fine.
So if you're still having this problem, try opening the C:\WINDOWS\TEMP directory on your computer. Once Windows changes the permissions on that folder so that your user account is allowed to access it, ApprovedWorkman.exe (which is running with the permissions of your user account) should also be able to access it, and can store its temporary files where it needs to.