  Recently several workers have attempted determinations of the so-called
magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap
equation, using a free massive propagator as input. Self-consistency is
attained only on-shell, because the usual Feynman-graph construction is
gauge-dependent off-shell. We examine two previous studies of the pinch
technique proper self-energy, which is gauge-invariant at all momenta, using a
free propagator as input, and show that it leads to inconsistent and unphysical
result. In one case the residue of the pole has the wrong sign (necessarily
implying the presence of a tachyonic pole); in the second case the residue is
positive, but two orders of magnitude larger than the input residue, which
shows that the residue is on the verge of becoming ghostlike. This happens
because of the infrared instability of d=3 gauge theory. A possible alternative
one-loop determination via the effective action also fails. The lesson is that
gap equations must be considered at least at two-loop level.
