Is there a conflict between causality and diamagnetism?

There is a long-standing apparent conflict between the existence of diamagnetism and causality as expressed through the Kramers-Kronig relations. In essence, using causality arguments, along with a small number of seemingly well-justified assumptions, one can show that diamagnetism is impossible. However, experiments show diamagnetic responses from magnetic media. We present a resolution to this issue, which also explains the absence of observed dia-electric responses in media. In the process, we expose some of the short-comings in earlier analyses that have kept the paradox alive.