I'm having the same problem. I've checked and double checked my permissions and they all seem to be just fine. I have the links.db.bak in my data folder and that hasn't helped either. Any help that could be provided would be very much appreciated. Below is the error message I have been receiving.
Backing up database . . .
Backing up links, category and email database (File::Copy) ...
CGI ERROR==========================================Error Message : Unable to copy links backup. Reason: No such file or directoryScript Location : /home/sites/mysite.com/cgi-bin/links/admin/nph-build.cgiPerl Version : 5.006001