The post-main-sequence eclipsing binary NN Serpentis was recently announced as the potential host of at least two massive planetary companions. In that work, the authors put forward two potential architectures that fit the observations of the eclipsing binary with almost identical precision. In this work, we present the results of a dynamical investigation of the orbital stability of both proposed system architectures, finding that they are only stable for scenarios in which the planets are locked in mutual mean motion resonance. In the discovery work, the authors artificially fixed the orbital eccentricity of the more massive planet, NN Ser (AB) c, at 0. Here, we reanalyse the observational data on NN Serpentis without this artificial constraint, and derive a new orbital solution for the two proposed planets. We detail the results of further dynamical simulations investigating the stability of our new orbital solution, and find that allowing a small non-zero eccentricity for the outer planet renders the system unstable. We conclude that although the original orbits proposed for the NN Serpentis planetary system prove dynamically feasible, further observations of the system are vital in order to better constrain the system's true architecture.