DTC P1065: ECM Power Supply Circuit (Back-Up): Description
WARNING: This page is about a different car, the 2002 Nissan Maxima and 2002 Infiniti I35. However, it is still accessible from the selected car via links, so may be relevant.
Battery voltage is supplied to the ECM even when the ignition 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.