iTunes sync does NOT automatically back up iPad 2

I'm using the latest version of iTunes (11.0.4) on an iMac with the latest version of Mountain Lion (10.8.4) and an iPad 2 with the latest firmware (iOS 6.1.3). When I sync the iPad, the process consists of only 3 steps (waiting for sync to start, preparing for sync, waiting for changes to be synced) and omits the usual automatic backup at the start (even though I have "Automatically Back Up to this comupter" checked and all my other devices - two iPhone 4S's, an original iPad, and a 3rd gen "New iPad" - backup during sync just fine).

This iPad is also experiencing wifi sync issues (won't automatically sync, does not even display the button for "sync now" in Settings, but shows up wirelessly in iTunes and can be synced from there no problem) that I'm not sure are related but could be...

Any ideas?