Large amplitude oscillatory shear (LAOS) experiments on molten high-density polyethylene (HDPE) conducted by Hatzikiriakos and Dealy have shown that the shear stress response is highly unstable above a critical shear stress amplitude of sigma(c) = 0.09 MPa. The contour of this critical stress amplitude on a Pipkin diagram is termed the slip isopleth. For stresses well below the slip isopleth, transient network theory has been shown to describe the LAOS behavior of this material accurately. However, the slip isopleth predicted by this theory is well below the measured isopleth. This discrepancy suggests that there could be a region on a Pipkin plot, where wall slip can occur, without giving rise to unstable stresses.