The existence of ultrafast rotating neutron stars (spin period P less than
or similar to1 ms) is expected on the basis of current models for the secul
ar evolution of interacting binaries, although they have not been detected
yet. Their formation depends on the quantity of matter accreted by the neut
ron star which, in turn, is limited by the mechanism of mass ejection from
the binary. An efficient mass ejection can avoid the formation of ultrafast
pulsars or their accretion-induced collapse to a black hole. We propose th
at significant reductions of the mass transfer rate may cause the switch-on
of a radio pulsar phase, whose radiation pressure may be capable of ejecti
ng 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 b
een reached, any further accretion, even if the original transfer rate is r
estored, thus limiting the minimum spin period attainable by the neutron st
ar. We show that close systems (orbital periods P-orb similar to 1 hr) are
the only possible hosts for ultrafast spinning neutron stars. This could ex
plain why ultrafast radio pulsars have not been detected so far, as the det
ection of pulsars with very short spin periods in close systems is hampered
, in current radio surveys, by strong Doppler modulation and computational
limitations.