In this paper, we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non-linear autoregressive control systems. The size of the structural uncertainty is characterized by multiple Lipschitz constants (say L-1, L-2,..., L-p) of the uncertain non-linear function. It is shown that if L-1, L-2,..., L-p satisfy certain algebraic conditions, then there exists no globally stabilizing feedback control law for the corresponding uncertain systems. The result here is an extension of the previous result obtained by Zhang and Guo (2002).