  We investigate the replica trick for the microscopic spectral density,
$\rho_s(x)$, of the Euclidean QCD Dirac operator. Our starting point is the
low-energy limit of the QCD partition function for $n$ fermionic flavors (or
replicas) in the sector of topological charge $\nu$. In the domain of the
smallest eigenvalues, this partition function is simply given by a U(n) unitary
matrix integral. We show that the asymptotic behavior of $\rho_s(x)$ for $x \to
\infty$ is obtained from the $n\to 0$ limit of this integral. The smooth
contributions to this series are obtained from an expansion about the replica
symmetric saddle-point, whereas the oscillatory terms follow from an expansion
about a saddle-point that breaks the replica symmetry. For $\nu =0$ we recover
the small-$x$ logarithmic singularity of the resolvent by means of the replica
trick. For half integer $\nu$, when the saddle point expansion of the U(n)
integral terminates, the replica trick reproduces the exact analytical result.
In all other cases only an asymptotic series that does not uniquely determine
the microscopic spectral density is obtained. We argue that bosonic replicas
fail to reproduce the microscopic spectral density. In all cases, the exact
answer is obtained naturally by means of the supersymmetric method.
