  We have investigated whether the lack of X-ray pulsations from most neutron
star (NS) low-mass X-ray binaries (LMXBs) could be due to the extension of
their inner disc to the NS surface. To estimate the inner disc radii, we have
employed the model, recently proposed to account for the torque reversals of
LMXBs. In this model, the inner disc radius depends on the spin period as well
as the dipole moment and the mass inflow rate of the disc. Our model results
indicate that most LMXBs have mass accretion rates above the minimum critical
rates required for the inner disc to reach down to the NS surface and thereby
quench the pulsed X-ray emission. For most sources X-ray pulsations are allowed
when the period decreases below a certain critical value. For the same
parameters, the model is also consistent with the observed X-ray luminosity
ranges of the individual accreting millisecond X-ray pulsars (AMXPs). The
paucity of AMXPs compared to the majority population of non-pulsing LMXBs is
explained, as well as the fact that AMXPs are transient sources.
