Resilience is regarded as an essential design objective of a wide range of systems in modern society. This work is based on a vision that networks of mobile energy storage systems could provide an alternative off-grid power system design for rural and underdeveloped regions. To evaluate the resiliency of networked energy storage systems under overload failure, a model of concurrent cascading failure and healing processes is developed and demonstrated. Two resilience metrics are used to evaluate the resilience of a real-world network, namely the recovery level at a specified time and the recovery time. The simulations generate system trajectories at each time step. We explore the dependence of the system behavior on different model parameters that capture key recovery strategies. The success probability of the recovery of a failed node needs to be high enough for the network to restore its original functionality. Similarly, the increase in recovery budget parameter also leads to faster and higher recovery levels. However, in most cases, there appears to be upper limits for both parameters, beyond which any further increase could not improve the recovery performance. There is an optimum portion of the loads of the active neighboring nodes that will be carried by the newly recovered node that results in the shortest recovery times or highest recovery levels. Our work sheds light on how to enhance networked systems resiliency by considering the optimization of various model parameters.