Growing evidence suggests that reward prospect promotes cognitive stability in terms of increased context or cue maintenance. In 3 Experiments, using different versions of the AX-continuous performance task, we investigated whether this reward effect comes at the cost of decreased cognitive flexibility. Experiment 1 shows that the reward induced increase of cue maintenance perseverates even when reward is no longer available. Experiment 2 shows that this reward effect not only survives the withdrawal of reward but also delays the adaptation to changed task conditions that make cue usage maladaptive. And finally in Experiment 3, it is shown that this reduced flexibility to adapt is observed in a more demanding modified version of the AX-continuous performance task and is even stronger under conditions of sustained reward. Taken together, all 3 Experiments thus speak to the idea that the prospect of reward increases cue maintenance and thereby cognitive stability. This increased cognitive stability however comes at the cost of decreased flexibility in terms of delayed adaptation to new reward and task conditions.