Recently, various Deep Neural Network (DNN) models have been proposed for environments like embedded systems with stringent energy constraints. The fundamental problem of determining the robustness of a DNN with respect to its energy consumption (energy robustness) is relatively unexplored compared to accuracy-based robustness. This work investigates the energy robustness of Adaptive Neural Networks (AdNNs), a type of energy-saving DNNs proposed for many energy-sensitive domains and have recently gained traction. We propose EREBA, the first black-box testing method for determining the energy robustness of an AdNN. EREBA explores and infers the relationship between inputs and the energy consumption of AdNNs to generate energy surging samples. Extensive implementation and evaluation using three state-of-the-art AdNNs demonstrate that test inputs generated by EREBA could degrade the performance of the system substantially. The test inputs generated by EREBA can increase the energy consumption of AdNNs by 2,000% compared to the original inputs. Our results also show that test inputs generated via EREBA are valuable in detecting energy surging inputs.