Repeated neuropsychological measurements, such as mini-mental state examination (MMSE) scores, are frequently used in Alzheimer’s disease (AD) research to study change in cognitive function of AD patients. A question of interest among dementia researchers is whether some AD patients exhibit transient “plateaus” of cognitive function in the course of the disease. We consider a statistical approach to this question, based on irregularly spaced repeated MMSE scores. We propose an algorithm that formalizes the measurement of an apparent cognitive plateau, and a procedure to evaluate the evidence of plateaus in AD using this algorithm based on applying the algorithm to the observed data and to data sets simulated from a linear mixed model. We apply these methods to repeated MMSE data from the Michigan Alzheimer’s Disease Research Center, finding a high rate of apparent plateaus and also a high rate of false discovery. Simulation studies are also conducted to assess the performance of the algorithm. In general, the false discovery rate of the algorithm is high unless the rate of decline is high compared with the measurement error of the cognitive test. It is argued that the results are not a problem of the specific algorithm chosen, but reflect a lack of information concerning the presence of plateaus in the data.