Modern aerospace vehicles are expected to perform beyond their conventional flight envelopes and exhibit the robustness and adaptability to operate in uncertain environments. Augmenting proven lower level control algorithms with adaptive elements that exhibit long term learning could help in achieving better adaptation performance while performing aggressive maneuvers. The current adaptive methodologies which use Neural Network based control methods use only the instantaneous states to tune the adaptive gains. This results in a rank one limitation on the adaptive law. In this paper we propose a novel approach to adaptive control, which uses the current or the online information as well as stored or background information for adaptation. We show that using a combined online and background learning approach it is possible to overcome the rank one limitation on the adaptive law resulting in faster adaptation to the unknown dynamics. Furthermore, we show that using combined online and background learning methods it is possible to guarantee long term learning in the adaptive flight controller, which enhances performance of the controller when it encounters a maneuver that has been performed in the past. We use Lyapunov based methods for showing boundedness of all signals for a proposed method. The performance of the proposed method is evaluated in the high fidelity simulation environment for the GTMAX UAS maintained by the Georgia Tech UAV lab. The simulation results show that the proposed method exhibits long term learning and faster adaptation leading to better performance of the UAS flight controller.