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AD5821A load current when Vdd=0

I am using an AD5821A to provide a custom current pulse through an IR LED for an engineering prototype. The microcontroller uses a LiPo battery for a power source. I use the 3.3V regulator on the uC board for Vdd, and a direct connection from the battery through the LED (plus a series current measuring resistor) to ISINK. DGND and AGND are shared, tied back to the - battery terminal. The setup works perfectly when the uC is on. I use the XSHUTDOWN pin to bring the LED current to zero. But when I "turn off" the system (disable the on-board 3.3V regulator), I see current flowing through the LED. In this state, I suppose XSHUTDOWN could be floating, but even if I tie XSHUTDOWN to GND in the off state, I still get current through the LED. This is more of an annoyance than a progress limiting problem as I come back the next day to a dead battery. Is there a solution other than a physical switch to disconnect the battery from the system?