Andersson et al. and Bildsten proposed that the spin of accreting neutron stars is limited by removal of angular momentum by gravitational radiation which increases dramatically with the spin frequency of the star. Both Bildsten and Andersson et al. argued that the r-modes of the neutron star for sufficiently quickly rotating and hot neutron stars will grow due to the emission of gravitational radiation, thereby accounting for a time varying quadrupole component to the neutron star's mass distribution. However, Levin later argued that the equilibrium between spin-up due to accretion and spin-down due to gravitational radiation is unstable, because the growth rate of the r-modes and consequently the rate of gravitational wave emission is an increasing function of the core temperature of the star. The system executes a limit cycle, spinning up for several million years and spinning down in less than a year. However, the duration of the spin-down portion of the limit cycle depends sensitively on the amplitude at which the nonlinear coupling between different r-modes becomes important. As the duration of the spin-down portion increases the fraction of accreting neutron stars which may be emitting gravitational radiation increases while the peak flux in gravitational radiation decreases. Depending on the distribution of quickly rotating neutron stars in the Galaxy and beyond, the number of gravitational emitters detectable with LIGO may be large.