Even if it is already set that way, I'm suggesting you change it to something else (to rewrite that preference file), such as "ignore." Once you see that it mounts to the desktop consistently without taking any action, select Open iTunes again.
If it is still unreliable when set to "ignore," I would consider other trouble-shooting. For example, you can create another admin user account in System Preferences Accounts. Log out and log in to that new account. Does the problem happen when using that account?