The kinetics of disorientation of polymer layered silicate nanocomposites following alignment of the silicate layers by prolonged large amplitude oscillatory shear are examined using linear viscoelastic measurements. Nanometer thick disks with diameters of 30 nm, 0.3-0.6 mum, and 5 mum dispersed in polymer matrices exhibit disorientation kinetics that are non-Brownian. The disorientation process exhibits signatures of aging observed in soft-colloidal glasses and is shown to be independent of temperature, nanoparticle size, and chemical details, viscoelasticity and molecular weight of the polymeric matrix.