One partner says "Fine" meaning resolution; the other hears surrender. The word is shared; the affective uptake is not. We formalize this as **affective meaning divergence** (AMD), the total-variation distance between interlocutors’ anchor-conditioned affect distributions. Building on speech-act theory, common-ground accumulation, and entropy-regularized game theory, we derive a logit best-response map whose dynamics undergo a *saddle-node bifurcation*: when 𝛽𝛼 > 4, a monotone increase in AMD-driven load produces an abrupt, hysteretic collapse of repair coordination. On Conversations Gone Awry (CGA-Wiki; N=652), derailing conversations exhibit critical-slowing-down (CSD) signatures across multiple levels: lexical divergence variance (p<0.001, d=0.36), AMD variance (p=0.001, d=0.26), and dialog-act repair variance (p=0.016, d=0.20), all significant after correction and stronger than toxicity and sentiment baselines. AMD provides a distinct temporal signature, with retrospectively measured variance peaking at the bifurcation point while toxicity variance peaks earlier, and is the only indicator grounded in the theoretical framework. Boundary-condition analysis on CGA-CMV (N=1,169) yields mixed but directionally consistent evidence.