Nanowire growth has generally relied on an initial particle of a catalyst such as Au to define the wire diameter and stabilize the growth. Self-catalyzed growth of III-V nanowires avoids the need for a foreign element, with the nanowire growing from the vapor via a droplet of the native group-III liquid. However, as suggested by Gibbs phase rule, the absence of third element has a destabilizing effect. Here we analyze this system theoretically, finding that growth can be dynamically stable at pressures far above the equilibrium vapor pressure. Steady-state growth occurs via kinetic self-regulation of the droplet volume and wire diameter. In particular, for a given temperature and source-gas pressures there is a unique stable wire diameter and droplet volume, both of which decrease with increasing V/III ratio. We also examine the evolution of the droplet size and wire diameter toward the steady state as the wire grows and discuss implications for structural control.