We revisit the classical problem of the viscoelastic response of nematic (liquid crystal) polymers to small amplitude oscillatory shear. A multiple time scale perturbation analysis is applied to the Doi-Hess mesoscopic orientation tensor model to describe key features observed of longtime experiments, both physical (Moldenaers and Mewis, J Rheol, 30:567-584, 1986; Larson and Mead, J Rheol, 33:1251-1281, 1989b) and numerical (herein). First, there is a very slow time scale drift in the envelope of oscillations of the major director; we characterize the mean director angle and the envelope of oscillation. Second, there are bistable asymptotic orientational states, distinguished in that they are precisely the zero-stress orientational distributions noted in Larson and Mead (J Rheol, 33:185206, 1989a). Third, the drift dynamics and asymptotic mean director angle are determined by the initial orientation of the director, not by material properties; we characterize the domain of attraction of each bistable state. Finally, the director drift leads to a predicted longtime decrease in the storage and loss moduli, consistent with experimental observations.