The anisotropy of the diffusivity of water molecules, probed via H-1 nuclear magnetic resonance imaging techniques, is used to study the extremely slow dynamics in the nematic phase of synthetic Na-fluorhectorite platelets in aqueous suspension. The anisotropy of the diamagnetic susceptibility of the platelets Delta chi, and the torque experienced in an applied magnetic field, permit one to monitor the time evolution starting from two different initial conditions. The dynamics of the ordered platelets can be modeled by a one-dimensional Fokker-Planck equation, which permits a satisfactory description of the experimental results. From the torque-free evolution, one concludes that the process is diffusive with an extremely slow rotational diffusivity D-phi = 9.9 x 10(-3) rad(2)/h. The forced evolution requires a numerical solution of the full Fokker-Planck equation and yields an effective, per platelet, diamagnetic susceptibility anisotropy Delta chi = - 1.63 x 10(-20) J/T-2.