ABSTRACT The presence of some X-ray sources in the Galactic Centre region which show variability, but do not show outbursts in over a decade of monitoring has been used to argue for the presence of a large population of stellar mass black holes in this region. A core element of the arguments that these objects are accreting black holes is the claim that neutron stars (NSs) in low-mass X-ray binaries (LMXBs) do not have long transient recurrence times. We demonstrate in this paper that about half of the known transient LMXBs with clear signatures for NS primaries have recurrence times in excess of a decade for outbursts at the sensitivity of MAXI. We furthermore show that, in order to reconcile the expected total population of NS LMXBs with the observed one and with the millisecond radio pulsar (MSRP) population of the Galaxy, systems with recurrence times well in excess of a century for outbursts detectable by instruments like MAXI must be the dominant population of NS LMXBs, and that few of these systems have yet been discovered.