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.