Autonomous aerial manipulators have great potentials to assist humans or even fully automate manual labor-intensive tasks such as aerial cleaning, aerial transportation, infrastructure repair, and agricultural inspection and sampling. Reinforcement learning holds the promise of enabling persistent autonomy of aerial manipulators because it can adapt to different situations by automatically learning optimal policies from the interactions between the aerial manipulator and environments. However, the learning process itself could experience failures that can practically endanger the safety of aerial manipulators and hence hinder persistent autonomy. In order to solve this problem, we propose for the aerial manipulator a self-reflective learning strategy that can smartly and safely finding optimal policies for different new situations. This self-reflective manner consists of three steps: identifying the appearance of new situations, re-seeking the optimal policy with reinforcement learning, and evaluating the termination of self-reflection. Numerical simulations demonstrate, compared with conventional learning-based autonomy, our strategy can significantly reduce failures while still can finish the given task.