  We investigate the effects of bulk impurities on the electronic spectrum of
Weyl semimetals, a recently identified class of Dirac-type materials. Using a
$T$-matrix approach, we study resonant scattering due to a localized impurity
in tight binding versions of the continuum models recently discussed by Burkov,
Hook, and Balents, describing perturbed four-component Dirac fermions in the
vicinity of a critical point. The impurity potential is described by a strength
$g$ as well as a matrix structure $\Lambda$. Unlike the case in d-wave
superconductors, where a zero energy resonance can always be induced by varying
the impurity scalar and/or magnetic impurity strength, we find that for certain
types of impurity ($\Lambda$), the Weyl node is protected, and that a scalar
impurity will induce an intragap resonance over a wide range of scattering
strength. A general framework is developed to address this question, as well as
to determine the dependence of resonance energy on the impurity strength.
