This is shear thinning.
This kind of non-Newtonian behaviour is not really important for simple fluids like water at macroscopic scales, but it is readily observable in simulations of small systems on short timescales.
The physical reason for shear thinnning in water (at simulated timescales) is that water as a liquid has quite a complex structure where the molecules are interconnected in big hydrogen-bonded networks. These hydrogen bonds take a short while to develop (molecules have to reorient the right way to form a hydrogen bond), so the faster you shear, the less time the molecules have to grab onto their neighbors, the weaker the hydrogen bonding and thus the lower the viscosity.
The same occurs in solutions of polymers and the like, because their long chains get entangled if given enough time to do so. You won't see much shear thinning in nice simple fluids made of isotropic spheres like the Lennard-Jones fluid.
Apart from true shear thinning, you can also see artifacts due to inadequate thermostatting. Shearing the fluid injects a considerable amount of energy into the system. This can disturb energy equipartitioning between different degrees of freedom or make it difficult for the thermostat to hold the temperature constant. Viscosity depends a whole lot on temperature, so any temperature disturbance is going to affect the results. (This becomes a big problem when you go to excessively high shear rates.)
