A low-order dynamical model that demonstrates the stable property of the tropical cyclone (TC) maximum potential intensity (MPI) equilibrium under the wind-induced surface heat exchange feedback was recently presented by Kieu. In this study, an alternative TC-scale model that allows for the gradient wind imbalance in the planetary boundary layer is proposed to further examine the stability of the MPI equilibrium. Despite different balanced assumptions, it is shown that the new TC-scale model possesses a similar MPI equilibrium with the same asymptotic stability. The structurally stable property of the MPI equilibrium is held for a range of the model parameters, regardless of the model initial conditions or numerical configurations. In addition, an explicit dependence of the MPI on the environmental lapse rate is obtained from the new TC-scale model, which reveals subtle impacts of the tropospheric stratification on TC intensity beyond the traditional MPI framework. The existence and interpretation of two distinct time scales during TC development will be also discussed.