We discuss the implications of late flares following GRBs for determining the nature of the central engine. We argue that since the flare timescales are much longer than naturally expected for a stellar mass compact object, progenitor systems containing a non-compact star are favored for short bursts displaying minute-long flares. For the case of short bursts, we argue that a minute-long flare time scale may be naturally explained if the progenitor is a binary system consisting of a neutron star and a non-compact companion, e.g. a low mass X-ray binary. In this scenario, the neutron star accretes mass and angular momentum from its companion until it undergoes accretion-induced collapse to a black hole or quark star. Due to its rapid spin when it collapses, a small torus of neutron star material forms and accretes on a viscous time. The burst itself is expected to be short, (τ <~1s), but the relativistic flow it accelerates hits the companion producing a minute-long flare. The delay between the GRB and beginning of the flare is given by the light travel time from the collapsed neutron star to the surface of the companion, tens of seconds, while the duration is given by the time for the relativistic shock to cross the star, a few minutes. No supernova-like emission is expected in this model. The progenitor systems are expected in both old and young stellar populations, consistent with the observed locations of short bursts in elliptical and star-forming galaxies. For long bursts, late flares are naturally explained by late accretion episodes if the massive stellar progenitor is not entirely disrupted during outburst.