The multitask diffusion LMS algorithm is an efficient strategy to address distributed estimation problems that are multitask-oriented in the sense that the optimum parameter vector may not be the same for every cluster of nodes. In this work, we explore the adaptation and learning behavior of the algorithm under asynchronous conditions when networks are subject to various sources of uncertainties, including random link failures and agents turning on and off randomly. We conduct a mean-square-error performance analysis and examine how asynchronous events interfere with the learning performance.