Long-horizon human pursuits (e.g., lifelong projects, scientific careers, entrepreneurship, elite training) sometimes show a striking pattern: persistence with low or zero immediate reward for extended periods, punctuated by sudden, intense bursts of goal-directed activity when opportunities arise. Classical reinforcement learning (RL) and canonical motivational theories — which emphasize reward prediction errors, temporal discounting, and reward-driven value updating — struggle to capture this “enduring yet conditional” persistence. Here we formalize and defend a neurocomputational hypothesis we call Conditionally Stable Motivation (CSM). CSM posits that (i) certain high-order goals are encoded as stable latent value attractors (state components, not ephemeral reward signals), (ii) a latent opportunity set mediates whether the goal’s motivational potential remains active, and (iii) neural circuits implement a two-mode control policy (maintenance vs. exploitation) governed by the opportunity set, with dopaminergic signals acting primarily as opportunity indicators rather than pure reward prediction errors in this regime. We present a precise mathematical model (state augmentation, motivational potential, policy switching rules), map model components to plausible neural substrates (vmPFC, dlPFC, ACC, ventral striatum/VTA), derive empirical predictions, and outline experiments and simulation paradigms for validation. We argue that CSM (a) reconciles long-horizon persistence with sparse rewards, (b) makes falsifiable neurophysiological predictions distinct from standard RL, and (c) provides a framework for understanding both adaptive persistence and pathological forms of unyielding pursuit. Keywords: long-horizon goals, motivation, vmPFC, dopamine, reinforcement learning, opportunity space, hierarchical control, theoretical neuroscience