The capability to autonomously track a non-cooperative target is a key technological requirement for micro aerial vehicles. In this paper, we propose an output feedback control scheme based on deep reinforcement learning for controlling a micro aerial vehicle to persistently track a flying target while maintaining visual contact. The proposed method leverages relative position data for control, relaxing the assumption of having access to full state information which is typical of related approaches in literature. Moreover, we exploit classical robustness indicators in the learning process through domain randomization to increase the robustness of the learned policy. Experimental results validate the proposed approach for target tracking, demonstrating high performance and robustness with respect to mass mismatches and control delays. The resulting nonlinear controller significantly outperforms a standard model-based design in numerous off-nominal scenarios.