Animal behavior is motivated by internal drives, such as thirst and hunger, generated in hypothalamic neurons that project widely to many brain areas. We find that water-restricted mice maintain stable, high-level contrast sensitivity and brief reaction time while performing a visual task, but then abruptly stop and become disengaged. Mice consume a significant amount of water when freely provided in their home cage immediately after the task, indicating that disengagement does not reflect cessation of thirst. Neuronal responses of V1 neurons are reduced in the disengaged state, but pupil diameter does not decrease, suggesting that animals' reduced level of arousal does not drive the transition to disengagement. Our findings indicate that satiation level alone does not have an instructive role in visually guided behavior and suggest that animals' behavior is governed by cost-benefit analysis that can override thirst signals.