  Many topologically non-trivial systems have been recently realized using
electromagnetic, acoustic, and other classical wave-based platforms. As the
simplest class of three-dimensional topological systems, Weyl semimetals have
attracted significant attention in this context. However, the robustness of the
topological Weyl state in the presence of dissipation, which is common to most
classical realizations, has not been studied in detail. In this paper, we
demonstrate that the symmetry properties of the Weyl material play a crucial
role in the annihilation of topological charges in the presence of losses. We
consider the specific example of a continuous plasma medium and compare two
possible realizations of a Weyl-point dispersion based on breaking
time-reversal symmetry (reciprocity) or breaking inversion symmetry. We
theoretically show that the topological state is fundamentally more robust
against losses in the nonreciprocal realization. Our findings elucidate the
impact of dissipation on three-dimensional topological materials and
metamaterials.
