According to the regulator datasheet the "dropout voltage" is at least 5mV, up to 400mV (dependent on the current draw):
The current drawn by the EMC2112 is at least 200uA, up to 1mA (that's a lot, I don't think the current draw is that much in practice):
I've no idea how big the actual current draw is. In worst case the voltage drop could be as high as 400mV. In this worst case scenario the EMC2112 cannot be powered properly anymore:
BTW for someone who does not know what dropout voltage is: What is the Dropout Voltage of a Regulator?