There is tantalizing evidence that some mechanically driven stratified flows tend towards a state of constant mixing efficiency. We provide insight into the energy balance leading to the constant mixing efficiency and isolate the responsible mechanism. The work presented demonstrates an important mixing efficiency regime for periodically forced externally driven stratified flows. Externally forced stratified turbulent mixing is often characterized by the associated eddies within the flow, which are the dominant mixing mechanism (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431–471). Here, we study mixing induced by vortex rings in order to characterize the mixing induced by an individual eddy. By generating a long sequence of independent vortex-ring mixing events in a density-stratified fluid with a sharp interface, we determine the mixing efficiency of each ring. After an initial adjustment phase, we find that the mixing efficiency of each vortex ring is independent of the Richardson number. By studying the mixing mechanism here, we demonstrate consistent features of a volumetrically confined, periodically forced external mixing regime.