Hydroxide-exchange membrane (HEM) electrolyzers can produce green H2 with only earth-abundant catalysts and electrolyte-free (nominally pure) water feed, significantly decreasing system cost and complexity. However, HEM technology suffers from short lifetimes, attributed in part to poor stability of anion-exchange polymers used in the membrane and catalyst layers. We use electrochemical analysis and ex situ characterization techniques to study anion-exchange-polymer degradation in electrolyzers. Using multiple ionomers, catalyst-layer additives, and electrolyte feed, we show how anode-ionomer oxidation is the dominant degradation mechanism for all HEM-based electrolyzer cells tested. We find improved device stability using oxidation-resistant catalyst-layer binders and propose new design strategies for advanced ionomer and catalyst-layer development.