  Context. Since the discovery of the first Accreting Millisecond X-ray Pulsar
SAX J1808.4-3658 in 1998, the family of these sources kept growing on.
Currently, it counts 22 members. All AMXPs are transients with usually very
long quiescence periods, implying that mass accretion rate in these systems is
quite low and not constant. Moreover, for at least three sources, a
non-conservative evolution was also proposed.
  Aims. Our purpose is to study the long term averaged mass-accretion rates in
all the Accreting Millisecond X-ray Pulsars discovered so far, to investigate a
non-conservative mass-transfer scenario.
  Methods. We calculated the expected mass-transfer rate under the hypothesis
of a conservative evolution based on their orbital periods and on the (minimum)
mass of the secondary (as derived from the mass function), driven by
gravitational radiation and/or magnetic braking. Using this theoretical
mass-transfer, we determined the expected accretion luminosity of the systems.
Thus, we achieved the lower limit to the distance of the sources by comparing
the computed theoretical luminosity and the observed flux averaged over a time
period of 20 years. Then, the lower limit to the distance of the sources has
been compared to the value of the distance reported in literature to evaluate
how reasonable is the hypothesis of a conservative mass-transfer.
  Results. Based on a sample of 18 sources, we found strong evidences of a
non-conservative mass-transfer for five sources, for which the estimated
distance lower limits are higher than their known distances. We also report
hints for mass outflows in other six sources. The discrepancy can be fixed
under the hypothesis of a non-conservative mass-transfer in which a fraction of
the mass transferred onto the compact object is swept away from the system,
likely due to the (rotating magnetic dipole) radiation pressure of the pulsar.
