  Recent studies found the densities of dark matter (DM) subhaloes which
surround nearby dwarf spheroidal galaxies (dSphs) to be significantly lower
than those of the most massive subhaloes expected around Milky Way sized
galaxies in cosmological simulations, the so called "too-big-to-fail" (TBTF)
problem. A caveat of previous work has been that dark substructures were
assumed to contain steep density cusps in the center of DM haloes even though
the central density structure of DM haloes is still under debate. In this
study, we re-examine the TBTF problem for models of DM density structure with
cores or shallowed cusps. Our analysis demonstrates that the TBTF problem is
alleviated as the logarithmic slope of the central cusp becomes shallower. We
find that the TBTF problem is avoided if the central cusps of DM haloes
surrounding dSphs are shallower than $r^{-0.6}$.
