  The existence of ultra-fast rotating neutron stars (spin period P < 1 ms) is
expected on the basis of current models for the secular evolution of
interacting binaries, though they have not been detected yet. Their formation
depends on the quantity of matter accreted by the neutron star which, in turn,
is limited by the mechanism of mass ejection from the binary. An efficient mass
ejection can avoid the formation of ultra-fast pulsars or their accretion
induced collapse to a black hole. We propose that significant reductions of the
mass-transfer rate may cause the switch-on of a radio pulsar phase, whose
radiation pressure may be capable of ejecting out of the system most of the
matter transferred by the companion. This can prevent, for long orbital periods
and if a sufficiently fast spin has been reached, any further accretion, even
if the original transfer rate is restored, thus limiting the minimum spin
period attainable by the neutron star. We show that close systems (orbital
periods P_orb \sim 1 hr are the only possible hosts for ultra-fast spinning
neutron stars. This could explain why ultra-fast radio pulsars have not been
detected so far, as the detection of pulsars with very short spin periods in
close systems is hampered, in current radio surveys, by strong Doppler
modulation and computational limitations.
