Multiple-target visual searches, where several targets may be present within a single search array, are susceptible to Subsequent Search Miss (SSM) errors—a reduction in second target detection after a first target has been found (an effect previously called Satisfaction of Search). SSM errors occur in critical search settings (e.g., radiology and airport security screening), creating concerns for public safety. To eradicate SSM errors it is vital to understand their cause(s), and the current study investigated a key proposed mechanism—searchers prematurely terminate their search after finding a first target. This proposed mechanism, termed the satisfaction account, was proposed over 50 years ago but there are no conclusive supporting data to date. “Satisfaction” has been typically assessed by comparing the total time spent on multiple-target trials to the time spent on single-target trials or by examining if search was immediately terminated after finding a first target. The current study investigated the satisfaction account by exploring variability in the time participants spent searching between finding a first target and self-terminating their search without finding a second target. This individual differences approach revealed that accuracy on a multiple-target search task related to how long participants searched after finding a first target. The relationship was highly significant, even when accounting for variation in participants’ attentional vigilance. This study provides evidence for the previously elusive satisfaction account and it adds to the growing understanding that SSM errors are a multifaceted problem.