We present a new deep multi-state Dynamic Recurrent Neural Network (DRNN) architecture for Brain Machine Interface (BMI) applications. Our DRNN is used to predict Cartesian representation of a computer cursor movement kinematics from open-loop neural data recorded from the posterior parietal cortex (PPC) of a human subject in a BMI system. We design the algorithm to achieve a reasonable trade-off between performance and robustness, and we constrain memory usage in favor of future hardware implementation. We feed the predictions of the network back to the input to improve prediction performance and robustness. We apply a scheduled sampling approach to the model in order to solve a statistical distribution mismatch between the ground truth and predictions. Additionally, we configure a small DRNN to operate with a short history of input, reducing the required buffering of input data and number of memory accesses. This configuration lowers the expected power consumption in a neural network accelerator. Operating on wavelet-based neural features, we show that the average performance of DRNN surpasses other state-of-the-art methods in the literature on both single- and multi-day data recorded over 43 days. Results show that multi-state DRNN has the potential to model the nonlinear relationships between the neural data and kinematics for robust BMIs.