  We consider non-linear massive gravity with two St\"uckelberg fields in which
the diffeomorphism invariance is broken spontaneously in two of the spacetime
directions. This theory admits a charged anti-de Sitter black brane solution
and has recently been used in holographic context as a bulk description of a
boundary field theory with momentum dissipation. Here we study the stability of
the black brane solution. We identify the physical degrees of freedom and
determine the healthy regions of the parameter space of the theory. We find
that there is a region in parameter space, where the theory suffers from ghost
instability. We recognise this as the reason for the instability found in the
previous works on holographic conductivity. We also rederive the previous
results for the holographic conductivity in a coordinate independent way.
