We present a detailed analysis of the orbital stability of the HD 181433 planetary system, finding it to exhibit strong dynamical instability across a wide range of orbital eccentricities, semimajor axes, and mutual inclinations. We also analyze the behavior of an alternative system architecture, proposed by Campanella, and find that it offers greater stability than the original solution, as a result of the planets being trapped in strong mutual resonance. We take advantage of more recent observations to perform a full refit of the system, producing a new planetary solution. The best-fit orbit for HD 181433 d now places the planet at a semimajor axis of 6.60+/-0.22 au, with an eccentricity of 0.469+/-0.013. Extensive simulations of this new system architecture reveal it to be dynamically stable across a broad range of potential orbital parameter space, increasing our confidence that the new solution represents the ground truth of the system. Our work highlights the advantage of performing dynamical simulations of candidate planetary systems in concert with the orbital fitting process, as well as supporting the continuing monitoring of radial velocity planet search targets.