I have been having same problem off and on since the end of March.
I've been through more steps than i care to count and I'm at the point where i believe the issue to be related to applemobiledevice helper.
I'm on win7 64 bit. hard drive has about 300 gigs free, the error thrown seems wrong given the amount of free space I have available.
I recently uninstalled itunes and apple mobile device helper, restarted pc and the sync worked... for about 2 days.
then the error cropped up again.
Next I tried unplugging my phone from computer and then simply stopping the apple mobile device helper exe (in task manager).
back ups resumed. I will be continuing to monitor the situation for a few days to see if any other obvious factors come out. I'm guessing that the issue lies within that exe somewhere and that some other application is causing it to fail and throw the error. Maybe it's RAM availability? I'm not sure yet but as mentioned, i'm going to continue to watch. I'm curious if the same works for anyone else out there (or if it works on a Mac)