I had the same issue on my Xubuntu 14.04 (Italian GUI). Obviously the other solutions in this page work, but they're a workaround.
Surprisingly I was able to solve it by logging out after having checked the checkbox ("Save the session for next accesses"), disabled automatic logon (i.e. the feature that allows to log on without typing the password) and the relogging on. After this, I disabled automatic logon, logged out and then logged in again, choosing this time not to use the saved session.
From then, all my desktop icons remain in the places I need them to be at each reboot, relog, etc.
Don't ask me why this happens, I'm happy enough to have solved my issue.
All the best