The last two decades have seen numerous investigations about the optimal design of mechanical stirrers for reverberation chambers (RC), with the aim of improving their stirring efficiency, without leading to a clear consensus on the reasons for their limited efficiency. This paper introduces a new criterion, by focusing on the incremental disorder introduced by mechanical stirrers, measured by their stirring coherence time, a measure of the rate of loss of coherence independent from the RC loading and excitation source. The model predicts that increasing losses would result in a loss of disorder, and therefore of stirring efficiency. Therefore, the stirring efficiency is not limited by a stirrer being too small (electrically) or too simple-shaped, but by the limited time they have to introduce disorder in a lossy RC. Experimental tests confirm the accuracy of the model's predictions under variable loading conditions. The model can predict the maximum loading for which a stirrer can be acceptably efficient. It applies to EMC testing of lossy devices, as well as over-the-air (OTA) tests for wireless communication devices, where absorbers are introduced in order to emulate different propagation environments.