  We investigate the dependence of pulse amplitudes of accreting millisecond
pulsars on the masses of the neutron stars. Because the pulsation amplitudes
are suppressed as the 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 the 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-Mdot systems. This mechanism
can also quantitatively explain the lack of pulsars in the majority of LMXBs.
