  For many years it has been recognized that the terminal stages of mass
transfer in a low-mass X-ray binary (LMXB) should cause the magnetosphere of
the accreting neutron star to expand, leading to a braking torque acting on the
spinning pulsar. After the discovery of radio millisecond pulsars (MSPs) it was
therefore somewhat a paradox (e.g. Ruderman et al. 1989) how these pulsars
could retain their fast spins following the Roche-lobe decoupling phase, RLDP.
Here I present a solution to this so-called "turn-off problem" which was
recently found by combining binary stellar evolution models with torque
computations (Tauris 2012). The solution is that during the RLDP the spin
equilibrium of the pulsar is broken and therefore it remains a fast spinning
object. I briefly discuss these findings in view of the two observed spin
distributions in the populations of accreting X-ray millisecond pulsars
(AXMSPs) and radio MSPs.
