This work further examines the rate at which potential vorticity in the core of a monotonic cyclone becomes vertically aligned and horizontally axisymmetric. We consider the case in which symmetrization occurs by the damping of a vortex Rossby (VR) wave. The damping of the VR wave is caused by its stirring of potential vorticity at a critical radius r_*, outside the core of the cyclone. The decay rate generally increases with the radial gradient of potential vorticity at r_*. Previous theories for the decay rate were based on "balance models'' of the vortex dynamics. Such models filter out inertia-buoyancy (IB) oscillations, i.e. gravity waves. However, if the Rossby number is greater than unity, the core VR wave can emit a frequency-matched outward propagating IB wave into the environment. To accurately account for this radiation, we here develop a theory for the decay rate that is based on the primitive equations. The decay rate is obtained analytically by considering conservation of wave activity (angular pseudomomentum). The analytical expression makes clear that the core VR wave experiences negative feedback from potential vorticity stirring at r_*, and positive feedback from IB wave radiation. The negative feedback will dominate (and the vortex will symmetrize) if the radial gradient of potential vorticity at r_* exceeds a small threshold. The possible relevance of this theory toward understanding the evolution of a tropical cyclone is discussed.