*

Reversible voltage control of electronic, magnetic, and optical properties over extraordinary ranges has recently been demonstrated in electrolyte-gated perovskite cobaltite films. This is achieved by reversibly cycling between perovskite (P) and oxygen-vacancy-ordered brownmillerite (BM) phases via electrochemical control. Most studies focus on the end states alone, however, i.e. P and BM, and little has been reported on the detailed gate voltage (V_g) dependence. Here, using ion gel gating of 10 unit-cell-thick La_0.5Sr_0.5CoO_3-δ films, we reveal that probing hysteresis loops around the P - BM transformation provides a wealth of new information. We combine source-drain current and gate current hysteresis loops with operando synchrotron X-ray diffraction, and transport and magnetotransport measurements. These reveal asymmetric hysteresis, non-monotonic transformation rates, and limits on reversibility, which we discuss and explain in detail. Minor hysteresis loops further enable the rational design of an optimized hysteresis cycle, resulting in ~10⁵ ON/OFF ratios with high reversibility.