  A two-component superconductor may hypothetically support a vestigial order
phase above its superconducting transition temperature, with rotational or
time-reversal symmetry spontaneously broken while remain non-superconducting.
This has been suggested as an explanation to the observed normal state
nematicity of the nematic superconductor $M_x$Bi$_2$Se$_3$. We examine the
condition for this vestigial order to occur within Ginzburg-Landau theory with
order parameter fluctuations, on both the nematic and chiral sides of the
theory. Contrary to prior theoretical results, we rule out a large portion of
parameter space for possible vestigial order. We argue that very extreme
anisotropy is one prerequisite for a stable vestigial phase, which is likely
not met in real materials.
