The Advanced Research WRF is used to examine the sensitivity of simulations of Typhoon Shanshan (2006) to changes in horizontal grid spacing at gray‐zone resolutions (7.5–1 km) and to choices of convective parameterization (CP) schemes. It is illustrated that fine resolution (3 to 1 km) runs feature a weak model convergence in tropical cyclone (TC) intensity than coarse resolution (7.5 to 5 km) runs, and the simulations using the Grell 3D ensemble CP (GR3D) exhibit a relatively strong model convergence, compared to the other three CP schemes. Further analyses reveal that model convergence relies on a number of factors that limit or promote TC intensification as resolution varies. Smaller radius of maximum wind (RMW) and thus smaller eyewall slope, along with smaller surface energy flux outside the eyewall and smaller eyewall asymmetries, are associated with finer resolution runs. These factors, especially the smaller RMW, promote the radial gradients of kinematical and microphysical attributes such as wind, pressure, latent heating, and mixing ratio of hydrometeors near the eyewall, causing growth of storm intensity, resulting in a weak model convergence. However, the impacts of the factors promoting storm intensification are notably different under different CP conditions, which are appreciably weaker in GR3D runs than in other three groups of CP experiments and responsible for a relatively strong model convergence in GR3D simulations. Overall, improvement of current CP schemes in simulation of TCs at gray‐zone resolutions is needed and targeted by a further study in future.