Nonlinear stability of magnetic islands in a helical plasma with resonant magnetic perturbation (RMP) is investigated using reduced magnetohydrodynamic equations including neoclassical viscosity. Coexistence of RMP-driven islands and the resistive interchange mode is numerically simulated. The self-healing of locked magnetic islands by neoclassical flows is observed. It is found that the curvature effect modifies the threshold of the self-healing, where the unfavorable curvature drives not only the interchange mode but also the curvature-driven tearing mode. An analytical model based on a Rutherford equation with a momentum equation is also introduced to understand the simulation results. Criterion of the self-healing considering the curvature effect is newly obtained.