An electrically operated aerosol-generating system may include a reservoir configured to hold a liquid aerosol-forming substrate, an atomizer assembly configured to vaporize the liquid aerosol-forming substrate to form an aerosol, and a pump configured to convey the liquid aerosol-forming substrate from the reservoir to the atomizer assembly. The reservoir may include a substantially rigid housing and an inlet valve that is configured to allow air into the reservoir based on a pressure difference between an interior of the housing and an exterior of the housing exceeding a threshold pressure difference. This improves the reliability and efficiency of delivery of liquid to the wick. The system may further include a robust reservoir that is configured to at least partially mitigate liquid leakage between the reservoir interior and the reservoir exterior.