We explore the regulation of star formation in star-forming galaxies through a suite of high-resolution isolated galaxy simulations. We use the smoothed particle hydrodynamics code gasoline, including photoelectric heating and metal cooling, which produces a multi-phase interstellar medium (ISM). We show that representative star formation and feedback sub-grid models naturally lead to a weak, sub-linear dependence between the amount of star formation and changes to star formation parameters. We incorporate these sub-grid models into an equilibrium pressure-driven regulation framework. We show that the sub-linear scaling arises as a consequence of the non-linear relationship between scaleheight and the effective pressure generated by stellar feedback. Thus, simulated star formation regulation is sensitive to how well vertical structure in the ISM is resolved. Full galaxy discs experience density waves which drive locally time-dependent star formation. We develop a simple time-dependent, pressure-driven model that reproduces the response extremely well.