  We study a dissipative gauge theory of nonrelativistic fermions in 2+1
dimensions at zero temperature by the Wilsonian renormalization-group method.
In this theory, we incorporate in the fermion propagator a new term of the form
$ i \kappa \cdot\sign(\omega)$ (where $\kappa$ is a parameter and $\omega$ is
the fermion frequency), which is usually induced by impurity effects. In the
previous papers, we studied this system for $\kappa = 0$, and showed that there
exists a non-Fermi-liquid infrared fixed point. In this paper, we address the
question whether this non-Fermi-liquid behavior remains stable or not in the
presence of impurity effects, i.e., the $\kappa$ term. Our results show that
the non-Fermi-liquid fixed point is unstable for $\kappa \neq 0$ and an
effective gauge coupling constant tends to vanish at low energies. However, in
intermediate energy scales, the behavior of correlation functions for $\kappa
\neq 0$ is controlled by the non-Fermi-liquid fixed point at $\kappa=0$, i.e.,
a crossover phenomenon appears. Physical implications of this phenomenon are
discussed.
