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Organic redox-active molecules are attractive as redox-flow battery (RFB) reactants because of their low anticipated costs and widely tunable properties. Unfortunately, many lab-scale flow cells experience rapid material degradation (from chemical and electrochemical decay mechanisms) and capacity fade during cycling (>0.1%/day) hindering their commercial deployment. In this work, we combine ultraviolet-visible spectrophotometry and statistical inference techniques to elucidate the Michael attack decay mechanism for 4,5-dihydroxy-1,3-benzenedisulfonic acid (BQDS), a once-promising positive electrolyte reactant for aqueous organic redox-flow batteries. We use Bayesian inference and multivariate curve resolution on the spectroscopic data to derive uncertainty-quantified reaction orders and rates for Michael attack, estimate the spectra of intermediate species and establish a quantitative connection between molecular decay and capacity fade. Our work illustrates the promise of using statistical inference to elucidate chemical and electrochemical mechanisms of capacity fade in organic redox-flow battery together with uncertainty quantification, in flow cell-based electrochemical systems.