DTC P1065: ECM Power Supply (Back-Up): Description
WARNING: This page is about a different car, the 2003 Nissan Altima. However, it is still accessible from the selected car via links, so may be relevant.
Battery voltage is supplied, even when the ignition switch is turned OFF, for the ECM memory function of the DTC memory, the air/fuel ratio feedback compensation value memory, the idle air volume learning value memory, etc.