The system will only pull coolant from the reservoir if the radiator is full. It's impossible to tell you what the problem without seeing the car, other than to say "you have a leak." You need to jack the car and support it with jack stands safely, then get underneath it and take a look. Is the leak towards the right or left side, forward of the engine or behind? Have the hoses been replaced recently, or are they original? Does the radiator cooling fan run when it should?
You may be able to borrow a cooling system pressure tester from your local auto parts store to pressurize the system to the proper pressure and see where coolant comes out, even on a cold engine.
-Rod