We motivate and study the robustness of fairness notions under refinement of transitions and places in Petri nets. We show that the classical notions of weak and strong fairness are not robust and we propose a hierarchy of increasingly strong, refinement-robust fairness notions. The hierarchy is based on the conflict structure of transitions, which characterizes the interplay between choice and synchronization in a fairness notion. The fairness notions are defined on non-sequential runs, but we show that the most important notions can be easily expressed on sequential runs as well. The hierarchy is further motivated by a brief discussion on the computational power of the fairness notions.