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An input to a system reveals a non-robust behaviour when, by making a small change in the input, the output of the system changes from acceptable (passing) to unacceptable (failing) or vice versa. Identifying inputs that lead to non-robust behaviours is important for many types of systems, e.g., cyber-physical and network systems, whose inputs are prone to perturbations. In this paper, we propose an approach that combines simulation-based testing with regression tree models to generate value ranges for inputs in response to which a system is likely to exhibit non-robust behaviours. We apply our approach to a network traffic-shaping system (NTSS) -- a novel case study from the network domain. In this case study, developed and conducted in collaboration with a network solutions provider, RabbitRun Technologies, input ranges that lead to non-robustness are of interest as a way to identify and mitigate network quality-of-service issues. We demonstrate that our approach accurately characterizes non-robust test inputs of NTSS by achieving a precision of 84% and a recall of 100%, significantly outperforming a standard baseline. In addition, we show that there is no statistically significant difference between the results obtained from our simulated testbed and a hardware testbed with identical configurations. Finally we describe lessons learned from our industrial collaboration, offering insights about how simulation helps discover unknown and undocumented behaviours as well as a new perspective on using non-robustness as a measure for system re-configuration.