Unable to turn off SRAM 23LC1024 connected to Arduino
As an experiment I would make sure ALL the pins are at 0V for reset. Power on ANY pin with a return path may provide enough parasitic power to prevent a proper shutdown. 

As has been pointed out you can use a I/O pin to power the device. This SRAM has 10mA operating current; enough to be supplied by an I/O pin. Then, with code only, you can make sure all pins go to 0V for the reset. This will also give you an extra power saving mode for free.