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 (ρth) 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 ρth hinders robust predictions and the interpretation of observations. A simulation of a (12 Mpc)3 volume with high ρth 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.