Neuromodulation is a pervasive biological process impacting neural activity at many scales. Changes in the concentration of a single neuromodulator can drastically alter the dynamics of a circuit. Nevertheless, how circuits can be both sensitive to the effects of neuromodulators, yet maintain stable behaviors in the face of constantly changing concentrations of them, is still poorly understood. Past work addressing this has focused on isolated circuits or individual neurons. In this paper, we study the effects of neuromodulation in the context of a complete brain-body-environment model. We use a genetic algorithm to find configurations of a dynamical neural network able to walk with and without the presence of an extrinsic neuromodulatory signal. We analyze, in some detail, networks, which break and cope under the effects of neuromodulation. We identify common stability mechanisms among successful networks, which correspond to previously proposed ideas. In addition, results indicate that proprioceptive feedback provides a stability mechanism for coping with neuromodulation that has not previously been considered in the literature.