Monte Carlo lattice gas simulations are performed to study sintering in a realistic dendritic platinum nanosheet. The morphological and topological transformations observed in the simulations are in good agreement with sintering experiments. Employing an intuitive method of quantifying surface area, the stability of the surface area of the dendritic nanosheets is analyzed. The surface area is found to have a double exponential decay, one decay corresponding to rapid coarsening of dendritic features into pores and the other decay corresponding to a slow disappearance of unstable pores. Long duration simulations indicate that the thickness of the dendritic nanosheet remains fairly stable. Stability simulations of a single model pore in a sheet establish that there exists a narrow range of sheet thickness and pore size combinations that produces stable holey sheets. Outside this parameter range pores either rapidly close or expand without bound. The thickness of the engineered dendritic platinum nanosheet and the size of the crevices between dendritic arms put the Pt sheet into this stable range, further corroborating the detailed simulations and explaining the persistence of pores observed in actual dendritic platinum nanosheets.