Persons with intellectual disability are a group at risk of being exposed to overly demanding problem-solving situations, which may produce learned helplessness. The research was based on the informational model of learned helplessness.The consequences of exposure to an unsolvable task and the ability to recognize the symptoms of cognitive exhaustion were tested in 120 students with mild intellectual disability. After the exposure to the unsolvable task, persons in the experimental group obtained lower results than the control group in the escape/avoidance learning task, but a similar result was found in the divergent thinking fluency task. Also, participants in the experimental group had difficulties recognizing the symptoms of the cognitive exhaustion state. After a week's time, the difference in escape/avoidance learning performance was still observed. The results indicate that exposure to unsolvable tasks may negatively influence the cognitive performance in persons with intellectual disability, although those persons may not identify the cognitive state related to lowered performance.