  The M\"obius energy is a well-studied knot energy with nice regularity and
self-repulsive properties. Stationary curves under the M\"obius energy gradient
are of significant theoretical interest as they they can indicate equilibrium
states of a curve under its own forces. In this paper, we consider stationary
symmetric helix pairs under the M\"obius energy. Through methods of complex
asymptotics, we characterize the limiting behavior of the M\"obius gradient as
the coiling ratio tends to infinity: the gradient will diverge in opposing
directions depending on whether the radius is less than or greater than
$\frac{1}{2}$.
  We conclude by discussing the implications to the more general
M\"obius-Plateau energy, where the energy of a curve, or pair of curves,
includes the area of the minimal surface bounded by them. Symmetric helix pairs
bound a helicoid between them, and applying our result shows that stationary
helicoids grow to radius $\frac{1}{2}$ from below as the coiling tends to
infinity.
