Power consumption of LD33CV voltage regulator
The LD33CV is the fixed 3.3V version of the LM1117. 

See page 6. Quiescent current at 25°C is typically 5mA, and could be as much as 10mA. That's the current with no output current being drawn. 

If your resolution on your meter is 0.01A then it may show zero. 

That will drain a smallish battery fairly quickly.