  We have performed a timing analysis of all the four X-ray outbursts from the
accreting millisecond pulsar SAX J1808.4-3658 observed so far by the PCA on
board RXTE. For each of the outbursts we derived the best-fit value of the time
of ascending node passage. We find that these times follow a parabolic trend,
which gives an orbital period derivative $\dot P_{\rm orb} = (3.40 \pm 0.18)
\times 10^{-12}$ s/s, and a refined estimate of the orbital period, $P_{\rm
orb} = 7249.156499 \pm 1.8 \times 10^{-5}$ s (reference epoch $T_0 =
50914.8099$ MJD). This derivative is positive, suggesting a degenerate or fully
convective companion star, but is more than one order of magnitude higher than
what is expected from secular evolution driven by angular momentum losses
caused by gravitational radiation under the hypothesis of conservative mass
transfer. Using simple considerations on the angular momentum of the system, we
propose an explanation of this puzzling result assuming that during X-ray
quiescence the source is ejecting matter (and angular momentum) from the inner
Lagrangian point. We have also verified that this behavior is in agreement with
a possible secular evolution of the system under the hypothesis of highly
non-conservative mass transfer. In this case, we find stringent constraints on
the masses of the two components of the binary system and its inclination. The
proposed orbital evolution indicates that in this kind of sources the neutron
star is capable to efficiently ablate the companion star, suggesting that this
kind of objects are part of the population of the so-called black widow
pulsars, still visible in X-rays during transient mass accretion episodes.
