Despite stochastic fluctuations, some genetic switches are able to retain their expression states through multiple cell divisions, providing epigenetic memory. We propose a novel rationale for tuning the functional stability of a simple synthetic gene switch through protein dimerization. Introducing an approximation scheme to access long-time stochastic dynamics of multiple-component gene circuits, we find that the spontaneous switching rate may exhibit greater than 8orders of magnitude variation. The manipulation of the circuit's biochemical properties offers a practical strategy for designing robust epigenetic memory with synthetic circuits.