  In this paper, we take into account the Gribov copies present in 3D
Yang-MIlls-Higgs theory with a constant vector background whose presence breaks
the Lorentz symmetry. The constant vector background is introduced within the
non-Abelian aether term. Here, we show that this term arises as a one-loop
correction. The influence of the aether coupling constant on the system is
treated afterwards. As a result, we find that for some values of it the theory
can be driven from a nonperturbative regime to a perturbative one. In this
paper, we work with the Higgs field in the fundamental representation and in
the Landau gauge.
