  The "too big to fail" problem is revisited by studying the tidal evolution of
populations of dwarf satellites with different density profiles. The high
resolution cosmological $\rm \Lambda CDM$ "ErisMod" set of simulations is used.
These simulations can model both the stellar and dark matter components of the
satellites, and their evolution under the action of the tides of a MW-sized
host halo at a force resolution better than 10 pc. The stronger tidal mass loss
and re-shaping of the mass distribution induced in satellites with $\gamma=0.6$
dark matter density distributions, as those resulting from the effect of
feedback in hydrodynamical simulations of dwarf galaxy formation, is sufficient
to bring the circular velocity profiles in agreement with the kinematics of
MW's dSphs. In contrast, in simulations in which the satellites retain cusps at
$z=0$ there are several "massive failures" with circular velocities in excess
of the observational constraints. Various sources of deviations in the
conventionally adopted relation between the circular velocity at the half light
radius and the one dimensional line-of-sight velocity dispersions are found.
Such deviations are caused by the response of circular velocity profiles to
tidal effects, which also varies depending on the initially assumed inner
density profile, and by the complexity of the stellar kinematics, which include
residual rotation and anisotropy. In addition tidal effects naturally induce
large deviations in the stellar mass-halo mass relation for halo masses below
$\rm 10^9 ~ M_{\odot}$, preventing any reliable application of the abundance
matching technique to dwarf galaxy satellites.
