The system has a leak somewhere, it might be the size of a pin hole - it is enough to cause this.
Firstly Im going to tell you how the cap works, it has one thick spring valve - this spring pressure is against about 14 psi pressure, once the engine warms up and the water expands it will apply pressure and the cap will let go - all this expanded water goes to the reserve bottle from the thin pipe.
When the engine shuts off and cools down he water shrinks and creates vacuum - this causes the small hat shaped valve to be sucked open - it then sips the water into the system until all the present vacuum is replaced with water.
The whole system should be checked for leaks - the small pipe should also have no pin hole leaks - if it has then hot water will move to the bottle but not back, this is because water is heavier than air - air is easier to suck - hence air is found in the radiator and to the eyes its empty. You should check this with a pressure cap adapter on a cold engine - pump up to 15 psi and check with soap water. You will find your leak
Now that you know what the cap does - you can troubleshoot the whole system easily.