LaSrCoO (LSCO) is known to undergo an electrochemically driven perovskite-to-brownmillerite transition with wide modulation of electronic, magnetic, thermal, and optical properties. However, the extended reversibility of this transition remains unproven, with repeated cycling leading to performance degradation via acid-etching, particularly in humid environments. Here, combining density functional theory with an out-of-the-box universal machine learning interatomic potential, the authors demonstrate that hydrogen insertion in LSCO is thermodynamically favorable over a wide range of conditions, but ultimately destabilizes the host structure towards decomposition. Metastable protonated phases are expected to exhibit significant structural expansion and band gap widening, mirroring the effect of oxygen vacancies and highlighting the need for caution when interpreting experimental results for electrochemically-gated LSCO and related materials.