In a microgrid, renewable energy sources (RES) exhibit stochastic behavior, which affects the microgrid continuous operation. Normally, energy storage systems (ESSs) are installed on the main branches of the microgrids to compensate for the load-supply mismatch. However, their state of charge (SoC) level needs to be balanced to guarantee the continuous operation of the microgrid in case of RES unavailability. This paper proposes a distributed forecast-based consensus control strategy for DC microgrids that balances the SoC levels of ESSs. By using the load-supply forecast of each branch, the microgrid operational continuity is increased while the voltage is stabilized. These objectives are achieved by prioritized (dis)charging of ESSs based on the RES availability and load forecast. Each branch controller integrates a load forecasting unit based on long short-term memory (LSTM) deep neural network that adaptively adjusts the (dis)charging rate of the ESSs to increase the microgrid endurability in the event of temporary generation insufficiencies. Furthermore, due to the large training data requirements of the LSTM models, distributed extended Kalman filter algorithm is used to improve the learning convergence time. The performance of the proposed strategy is evaluated on an experimental 380V DC microgrid hardware-in-the-loop test-bench and the results confirm the achievement of the controller objectives.