  We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$
instanton in continuum gauge theory. We find that there is a class of solutions
to the differential MA gauge condition with circular monopole loops of radius
$R$ centered on the instanton of width $\rho$. However, the MA gauge fixing
functional $G$ decreases monotonically as $R/\rho \rightarrow 0$. Its global
minimum is the instanton in the singular gauge. We point out that interactions
with nearby anti-instantons are likely to excite these monopole loops.
