Flying insects encounter turbulent environments, where chemotaxis along a concentration gradient makes little sense. Detection of the onset and offset of discrete odor pulses is then expected to become crucial for navigation, but it is not well understood how the olfactory system encodes the offset of the odor pulse. Previous works indicated that the duration of a male moth olfactory receptor neuron’s (ORN) spike firing response to pheromone stimuli greatly exceeds the pulse duration. However, these works were based on imprecise odor delivery systems. We built an odor delivery system capable of delivering much sharper pheromone stimuli. The stimuli evoked ORN firing responses that faithfully tracked the stimulus duration, provided the stimulus lasted at least 200 ms. A transient inhibition marked the termination of such stimuli. Shorter stimuli produced a firing response exceeding the stimulus duration. The response shapes could be explained by adaptation of the ORN on only two time scales. With simulations, we showed that the observed limits in stimulus offset detection propagate to the antennal lobe and are likely to be behaviorally significant. Our results increase the understanding of the mechanisms necessary for male moths to navigate through pheromone plumes.