  In this work we address the physics of individual three dimensional Weyl
nodes subject to a moderate concentration of disorder. Previous analysis
indicates the presence of a quantum phase transition below which disorder
becomes irrelevant and the integrity of sharp nodal points of vanishing
spectral density is preserved in this system. This statement appears to be at
variance with the inevitable presence of statistically rare fluctuations which
cannot be considered as weak and must have strong influence on the system's
spectrum, no matter how small the average concentration. We here reconcile the
two pictures by demonstrating that rare fluctuation potentials in the Weyl
system generate a peculiar type of resonances which carry spectral density in
any neighborhood of zero energy, but never at zero. In this way, the vanishing
of the DoS for weak disorder survives the inclusion of rare events. We
demonstrate this feature by considering three different models of disorder,
each emphasizing specific aspects of the problem: a simplistic box potential
model, a model with Gaussian distributed disorder, and one with a finite number
of $s$-wave scatterers. Our analysis also explains why the protection of the
nodal DoS may be difficult to see in simulations of finite size lattices.
