I've backed up COD Blackops with MM no problems but I do acknowledge your problem.
I had a similar problem backing up especially larger games with certain backup managers and found that by trying another manager, the problem would be sorted. So that could be a solution.
Other games on the other hand do take quite a long time to backup. Sega and Sonic All Start Racing for example at around 2GB takes several hours and there are a number of others like this. I backed up COD BO a long time ago so I can't recall if there was such an issue with that game but it could be. Solution - wait longer.
Another possible cause is that you're trying to backup a game to a location/drive with insufficient space - which can be tricky to determine with any real accuracy on a PS3 - especially if you've backed up and deleted a few things over time. Also, I recall trying to backup a game in the early days of JB'ing whilst there was a usb key attached to the PS3. The backup would seem to go on forever and then stop and it was only later that I found that I inadvertently had tried to backup to the usb key!
If none of the above applies to you then I guess you have be sure you are dealing with complete and clean data/discs.
Hope this is of some help. Good luck!
"We all agree your theory is crazy, but is it crazy enough?" - Neils Bohr