The presentation of one task increases the reaction time on a subsequent task, if stimulus onset asynchrony (SOA) between tasks is short. This psychological refractory period (PRP) effect is typically leveling off as SOA approaches 1 s, which has been documented both in classical laboratory paradigms and in simulated car driving. Here we report a more persistent effect on the subsequent task that goes well beyond the typical duration of the PRP effect. In a driving simulator, 120 healthy older participants followed a lead car that mostly drove at a constant speed. They had to maintain a regular distance from the lead car and had to brake when the lead car braked. Participants also engaged in several additional tasks during driving (two types of tasks: typing three-digit numbers, stating arguments on public issues). SOA between the braking task and the last preceding additional task was 11.49 s ± 1.99 (mean and standard deviation). In a control condition, the braking task was administered without additional tasks. Main performance outcome was Braking Reaction Time (RT, in s), as the interval between onset of brake lights of the lead car and the moment participants released the gas pedal. Additionally, foot movement time (MT, in s), i.e., the difference between gas pedal release and brake pedal onset, was considered for possible compensation behavior. Inter-vehicle distance to the lead car (in m) was taken into account as a moderator. We found that RT averaged 0.77 s without additional tasks, but averaged 1.45 s with additional tasks. This RT difference was less pronounced at smaller inter-vehicle distances, and was not compensated for by faster MT from the gas pedal to the brake pedal. We conclude that detrimental effects of additional tasks on subsequent braking responses can be more persistent than suggested by the PRP effect, possibly because of maintaining multiple task sets, requiring increased executive control. We further conclude that potential detrimental effects can be ameliorated at small inter-vehicle distances by mobilizing extra cognitive resources when response urgency is higher. As a practical implication of our study, distracting stimuli can have persisting detrimental effects on traffic safety.