Can you tell us what happens when you try to save the photos? Do you get a notification/error code or notice or does nothing happen? If it's a notice, what does it say?
If you don't get a notice, it may be that you haven't authorized Facebook to save photos. With the newest iOS (6.0 and higher), you have to specifically authorize Facebook (and other apps) so they can access the Photos. If you don't authorize, they won't even save. To check that Facebook is authorized, go to the Privacy tab in your Settings. Press that line and then press the line labeled "Photos." When that tab appears (it'll show all the apps that are authorized access to your photos) - find the Facebook line and ensure the button/switch is turned ON.
That should make it so you can save photos from Facebook. If so, yay. If not, holler back and we'll take another try...
Marilyn