We use cosmological hydrodynamical simulations of the APOSTLE project along with high-quality rotation curve observations to examine the fraction of baryons in {Lambda}CDM haloes that collect into galaxies. This galaxy formation efficiency correlates strongly and with little scatter with halo mass, dropping steadily towards dwarf galaxies. The baryonic mass of a galaxy may thus be used to place a lower limit on total halo mass and, consequently, on its asymptotic maximum circular velocity. A number of observed dwarfs seem to violate this constraint, having baryonic masses up to ten times higher than expected from their rotation speeds, or, alternatively, rotating at only half the speed expected for their mass. Taking the data at face value, either these systems have formed galaxies with extraordinary efficiency - highly unlikely given their shallow potential wells - or their dark matter content is much lower than expected from {Lambda}CDM haloes. This missing dark matter is reminiscent of the inner mass deficit of galaxies with slowly-rising rotation curves, but cannot be explained away by star formation-induced cores in the dark mass profile, since the anomalous deficit applies to regions larger than the luminous galaxies themselves. We argue that explaining the structure of these galaxies would require either substantial modification of the standard Lambda cold dark matter paradigm or else significant revision to the uncertainties in their inferred mass profiles, which should be much larger than reported. Systematic errors in inclination may provide a simple resolution to what would otherwise be a rather intractable problem for the current paradigm.