  We examine the formation of dark matter (DM) cores in dwarf galaxies
simulated with the EAGLE model of galaxy formation. As in earlier work, we find
that the star formation (SF) gas density threshold ($\rho_{\rm th}$) plays a
critical role. At low thresholds (LT), gas is unable to reach densities high
enough to dominate the gravitational potential before being dispersed by
feedback from supernovae. LT runs show little effect on the inner DM profile,
even in systems with extended and bursty SF, two ingredients often cited as
critical for core formation. For higher thresholds, gas is able to dominate the
gravitational potential before being ejected by feedback. This can lead to a
substantial reduction in the inner DM content, but only if the gas is
gravitationally important over an extended period of time, allowing the halo to
contract before gas removal. Rapid assembly and removal of gas in short SF
bursts is less effective at altering the inner DM content. Subsequent gas
accretion may draw DM back in and reform a cusp, unless SF is bursty enough to
prevent it, preserving the core. Thus, for the EAGLE SF+feedback model, there
is no simple relation between core formation and SF history, contrary to recent
claims. The dependence of the inner DM content of dwarfs on $\rho_{\rm th}$
hinders robust predictions and the interpretation of observations. A simulation
of a $(12 \rm \ Mpc)^3$ volume with high $\rho_{\rm th}$ results in dwarfs with
sizeable cores over a limited halo mass range, but with insufficient variety in
mass profiles to explain the observed diversity of dwarf galaxy rotation
curves.
