People often conduct visual searches in which multiple targets are possible (e.g., medical x-rays can contain multiple abnormalities). In this type of search, observers are more likely to miss a second target after having found a first one (a subsequent search miss). Recent evidence suggests that this effect may be due to a depletion of cognitive resources from tracking the identities and locations of found targets. Given that tracking moving objects is resource-demanding, would finding a moving target further increase the chances of missing a subsequent one? To address this question, we had participants search for one or more targets hidden among distractors. Subsequent search misses were more likely when targets and distractors moved throughout the display than when they remained stationary. However, when found targets were highlighted in a unique color, subsequent search misses were no more likely in moving displays. Together, these results suggest that the effect of movement was likely due to the increased cognitive demands of tracking moving targets. Overall, our findings reveal that activities that involve searching for moving targets (e.g., driving) are more susceptible to subsequent search misses than those that involve searching for stationary targets (e.g., baggage screening).