This paper proposes a time optimal control methodology to maximize the sustaining time of a power buffer. By improving the sustaining time, constant power load based active load instabilities are mitigated in DC micro-grids during a fault period. Starting from the energy and resistance domain modeling of the active load, time optimal control problem has been formulated to maximize the sustaining time and to minimize the state transient cost of the power buffer. The solution of the defined optimal control problem has been obtained using the Legendre-Gauss-Radau (LGR) direct orthogonal collocation method. Simulation results are presented to show the effectiveness of the proposed method.