Abstract The recurring devastation caused by extreme events underscores the need for reliable estimates of their intensity and frequency. Operational frequency and intensity estimates are very often obtained from generalized extreme value (GEV) distributions fitted to samples of annual maxima. GEV distributed random variables are “max-stable,” meaning that the maximum of a sample of several values drawn from a given GEV distribution is again GEV distributed with the same shape parameter. Long-period return value estimation relies on this property of the distribution. The data to which the models are fitted may not, however, be max-stable. Observational records are generally too short to assess whether max-stability holds in the upper tail of the observations. Large ensemble climate simulations, from which we can obtain very large samples of annual extremes, provide an opportunity to assess whether max-stability holds in a model-simulated climate and to quantify the impact of the lack of max-stability on very long period return-level estimates. We use a recent large ensemble simulation of the North American climate for this purpose. We find that the annual maxima of short-duration precipitation extremes tend not to be max-stable in the simulated climate, as indicated by systematic variation in the estimated shape parameter as block length is increased from 1 to 20 years. We explore how the lack of max-stability affects the estimation of very long period return levels and discuss reasons why short-duration precipitation extremes may not be max-stable.