Unmanned Aerial Vehicles (UAVs) can be utilized as aerial base stations to establish wireless communication networks in various challenging scenarios, such as emergency disaster areas and rural areas. Under large regions, the aerial communication networks would require UAVs to form wireless (backhaul) links among each other to provide end-to-end wireless services between two or more ground users (via one or more UAVs). Such UAV backhauling in aerial communication networks may be severely compromised if one or more UAVs are knocked off during the time of operation – it may be due to UAV hardware/software faults, limited battery, malicious attacks, etc. Deep reinforcement learning (DRL) has emerged as a powerful tool for learning tasks with large state and continuous action spaces. In this paper, we leverage emerging DRL to achieve reliable backhauling in an aerial communication network that remains functional and supports end-to-end wireless services even under various random and/or targeted UAV node failures. The proposed method (i) maximizes the reliability of UAV backhauling with joint consideration for communication coverage, (ii) learns the complex environment and its dynamics, and (iii) makes 3D positioning decisions for each UAV under the guidance of two deep neural networks. Our performance evaluation reveals that the proposed DRL approach outperforms the baseline method in terms of wireless coverage and network reliability against UAV failures.