Linear and nonlinear analyses were conducted to study the onset and growth of gravitational instability in an isolated porous medium. By considering the dissolution capacity of the isolated system, base concentration profiles were obtained analytically. Based on this base concentration field, linear stability equations were derived under the linear stability theory. The present stability analysis predicts that an isolated system is more stable than the conventional open system. In addition, the dissolution capacity of the isolated system suppresses the onset of instability. Unlike the previous study, the minimum Darcy-Rayleigh number to induce gravitational instability exists and it is a strong function of the dissolution capacity. However, the critical conditions for the high Darcy-Rayleigh number system are insensitive to the dissolution capacity. Based on the results of the linear analysis and the analytically obtained base concentration profile, fully nonlinear numerical simulations were also conducted for the case of Ra=103. The vertical development of the instability motion and the dissolution flux are significantly suppressed in the high dissolution capacity systems.