A few days ago my carrier rolled out the OTA Android Update 4.1.2.
I didn't want to lose root on my Samsung Galaxy Nexus after updating from 4.1.1 to the new 4.1.2 release and I installed OTA RootKeeper from Google Play.
The important step is to install and run RootKeeper before you do the update. Instructions on how to use RootKeeper can be found here.
This should work at least for the Samsung Galaxy Nexus running Android 4.1.2 without a custom recovery image.
After updating to the new Android version and rebooting your phone you have to start RootKeeper again to reactivate root. All you have to do is to select Restore Root and your phone is rooted again.