When an external magnetic field is applied to a diamagnetic materials, their atomic current loops will tend to align in such a way as to oppose the applied field. Diamagnetism is the residual magnetic behavior when materials are neither paramagnetic nor ferromagnetic and most materials are diamagnetic. Why don't these materials keep on repelled by a magnet? (e.g. we do see copper is repelled and fly away from a magnet)
Ok I'll give this one a go - the reason is that the effect is just not strong enough.
Andre Geim showed that in a strong enough magnetic field you can levitate a frog. Frogs are mostly water and water is diamagnetic.
You can also buy a kit from your local electronics store that has a piece of (strongly diamagnetic) pyrolytic carbon and a neodymium magnet and you can levitate the small piece of carbon above the magnet.
Bottom line is you need the right material and a strong enough magnetic field.