Galaxy Nexus Official 4.0.4 update and root Since the official 4.0.4 that be downloaded from Google's servers seems to be an update (39mb) can I update my rooted Galaxy Nexus wuthout losing root?
All OTA updates reset file permissions, so you'll lose root unless you take special precautions. Install OTA RootKeeper and make a backup of your su executable before applying this update. You'll be able to restore your root once update is finished.

Obviously, since this is an incremental update, you need to have a stock Nexus ROM. If you deleted or altered some system files, update may fail. 

I used Galaxy Nexus Toolkit to apply these updates, worked OK for me (and I kept my root).