My PS3 is out of space, and I was going to restore it to factory setting to get rid of all the game data since I can not find them. However when I went to copy my save data for Kingdoms of Amalur: Reckoning I noticed that it is copy protected. How can I restore my PS3 and not lose my game data?
I believe that the only viable solution would be paying for the shortest available Playstation Plus subscription, backing up your saves on the cloud and retrieving them after deleting all data on you PS3. The downside is that this costs money.
What I find strange is that you are having a hard time tracking down the content that is taking up all your space. I've had to free up some space more than once and I've always been able to track down unnecessary content. Try having a look at all of the following again:
The only other way I know to move copy-protected saves around is using the Data Transfer Utility, but it won't help you at all in this scenario.
Restoring your PS3 to factory state is rather drastic solution! You're bound to miss something and regret doing it later. Better to "uninstall" a game by deleting its installed data.
A game's installation data can usually be found in the Game Data Utility folder. If you scroll to an item, press triangle and choose "Information", it will tell you how much space that item is consuming. Choosing "Delete" will effectively uninstall that game and will free up space.
Another option is to increase the total space by upgrading the hard disk. Sony has made it very easy to upgrade the PS3's hard disk, and doing so does not invalidate your warranty. The Backup Utility feature (under Settings > System Settings) can be used to make a backup of all your data, then restore it after you've installed the new hard disk. The Backup Utility will restore your copy-protected saves as long as you are restoring the data to the same PS3 console (which you are if you are using it to upgrade the hard disk).