What makes an accretion-powered millisecond pulsar?

We investigate the dependence of pulse amplitudes of accreting millisecond pulsars on the masses of the neutron stars. Because pulsation amplitudes are suppressed as neutron stars become more massive, the probability of detection of pulsations decreases in systems that have been accreting for a long time. However, the probability of detectable pulsations is higher in transient systems where mass accretion is sporadic and the neutron star is likely to have a low mass. We propose this mechanism as the explanation of the small number of millisecond X-ray pulsars found to date, as well as their emergence as fast pulsars mostly in transient, low-M systems. This mechanism can also quantitatively explain the lack of pulsars in the majority of low-mass X-ray binaries.