The VY Scl stars (sometimes called `antidwarf novae') are cataclysmic variables, the light curves of which can be characterized by occasional drops from steady high states into low states lasting up to several hundred days. These low states probably result from episodes of low mass transfer from the companion star. The usual thermal-viscous disc instability picture suggests that sufficient mass should be left in the low-state disc to sustain dwarf nova eruptions for some time, even if no matter is transferred. However, such eruptions are not seen during VY Scl low states. We present simulations of the evolution of accretion discs in VY Scl systems, including the heating of the disc by radiation from the central white dwarf and boundary layer. The inner region of the accretion disc can be kept fully ionized by a moderately hot white dwarf, and remains hot even during low states. The transition radius between this hot inner region and the cool outer disc moves outward for higher white dwarf temperatures. For a white dwarf temperature T_WD = 20 000 K, inside-out outbursts occur during quiescence, starting at the transition radius. When T_WD = 40 000 K, the transition radius moves beyond the region where the disc surface density can build up to the critical value for outbursts, leaving a cool outer region which remains stably in the low state. Thus the observed presence of relatively hot white dwarfs in VY Scl stars explains why they show no dwarf-nova-type outbursts from the low state.