How did you get the car to the dealer? Did you jump start it and drive it or have it towed? If you jump started and drove it, the battery would be somewhat recharged by driving so it would not be really low when tested at the dealer unless it was truly defective (bad cell, internal short circuit, etc.). Since the replacement battery was also found dead after being parked, something is discharging the battery.
Do you routinely leave the car plugged in in the garage after charging? There is more residual current drawn by the various modules in the car when it is plugged in and not actively charging than when it is not plugged in. I don't know if the 2013 will turn on the DC-DC converter to recharge the 12-volt battery while the car is plugged in or not (I know the 2011/2012 models will not so they will completely discharge the 12-volt battery if left plugged in, but am not sure about later models).
Until you find the cause, I recommend that you unplug Bluetooth dongles or other devices from the OBDII port when you park the car to eliminate the possibility that something is interfering with the car's "sleep" mode and keeping modules active. I had a small control relay fail to drop out once in a while on the 2011. It kept power to the shift control module so it would probably have discharged the battery if it had failed when I parked for longer than overnight.
Silver LEAF 2011 SL rear ended (totaled) by in-attentive driver 1/4/2015 at 50,422 miles
Silver LEAF 2015 SL purchased 2/7/2015