  We consider the role that gauge symmetry breaking terms play on the continuum
limit of gauge theories in three dimensions. As a paradigmatic example we
consider scalar electrodynamics in which $N_f$ complex scalar fields interact
with a U(1) gauge field. We discuss under which conditions a gauge-symmetry
breaking term destabilizes the critical behavior (continuum limit) of the
gauge-invariant theory. We find that the gauge symmetry is robust at
transitions at which gauge fields are not critical. At charged transitions,
where gauge fields are critical, gauge symmetry is lost as soon as the
perturbation is added.
