Sum-product networks are a popular family of probabilistic graphical models that have been shown to achieve state-of-the-art performance in several tasks. When learning sum-product networks from scarce data, the obtained model may be prone to robustness issues, and where small variations of parameters could lead to different conclusions. We discuss the characteristics of sum-product networks as classifiers and study the robustness of them with respect to their parameters. Using a robustness measure to identify (possibly) unreliable decisions, we build a hierarchical approach where the classification task in testing time is deferred to another model if the outcome is deemed unreliable. We apply this approach on benchmark classification tasks across 47 datasets. Experiments show that the robustness measure can be a meaningful manner to build dynamic ensemble of classifiers and that our Hierarchical Sum-Product Network guarantees an improvement in accuracy.