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, Phys. Rev. B 84, 235126 (2011)], 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 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.