In this paper, we propose a closed-loop sensitivity-based approach to enhance the robustness of robotic non-prehensile dynamic manipulation tasks. The proposed method aims at fulfilling the transportation of an object, that is free to move on a tray-shaped robot end-effector, in face of not perfectly known nominal dynamic parameters. The approach is built up on taking the parameterized reference trajectory to be tracked as the optimization variable minimizing a norm of the task closed-loop sensitivity. The resulting optimal reference trajectory is inherently more robust to the parametric variations of object dynamic properties compared to a baseline trajectory execution. The tracking performance is assessed and validated along hardware experiments and an extensive simulation campaign assessing the superior robustness of our approach.