  The clumpiness of dark matter on sub-kpc scales is highly sensitive to the
tidal evolution and survival of subhaloes. In agreement with previous studies,
we show that N-body realisations of cold dark matter subhaloes with
centrally-divergent density cusps form artificial constant-density cores on the
scale of the resolution limit of the simulation. These density cores drive the
artificial tidal disruption of subhaloes. We run controlled simulations of the
tidal evolution of a single subhalo where we repeatedly reconstruct the density
cusp, preventing artificial disruption. This allows us to follow the evolution
of the subhalo for arbitrarily large fractions of tidally stripped mass. Based
on this numerical evidence in combination with simple dynamical arguments, we
argue that cuspy dark matter subhaloes cannot be completely disrupted by smooth
tidal fields. Modelling stars as collisionless tracers of the underlying
potential, we furthermore study the tidal evolution of Milky Way dwarf
spheroidal galaxies. Using a model of the Tucana III dwarf as an example, we
show that tides can strip dwarf galaxies down to sub-solar luminosities. The
remnant 'micro-galaxies' would appear as co-moving groups of metal-poor,
low-mass stars of similar age, embedded in sub-kpc dark matter subhaloes.
