This paper addresses a distributed real-time optimal power flow (RTOPF) strategy for DC microgrids. In this paper, we focus on the scenarios where local information sharing is conducted in stochastic communication networks subject to random failures. Most existing real-time optimal power flow (OPF) algorithms for the DC microgrid require all controllers to work in concert with a fixed network topology to maintain a zero gap between estimated global constraint violations. Thus, the high reliability of communication is required to ensure their convergence. To address this issue, the proposed RTOPF strategy tolerates stochastic communication failures and can seek the optimum with a constant step size considering the operation limitations of the microgrid. These aspects make the strategy suitable for real-time optimization, particularly when the communication is not reliable. In addition, this strategy does not require information from non-dispatchable devices, thereby reducing the number of sensors and controllers in the system. The convergence of the proposed strategy and the optimal equilibrium points are theoretically proven. Finally, simulations of a 30-bus DC microgrid are performed to validate the effectiveness of the proposed designs.