  We propose that Kozai's phenomenon is responsible for the long-term evolution
of stellar orbits near a supermassive black hole. We pursue the idea that this
process may be driven by a fossil accretion disc in the centre of our Galaxy,
causing the gradual orbital decay of stellar trajectories, while setting some
stars on highly elliptic orbits. We evolve model orbits that undergo repetitive
transitions across the disc over the period of ~10^7 years. We assume that the
disc mass is small compared to the central black hole, and its gravitational
field comparatively weak, yet non-zero, and we set the present values of
orbital parameters of the model star consistent with those reported for the S2
star in Sagittarius A*. We show how a model trajectory decays and circularizes,
but at some point the mean eccentricity is substantially increased by Kozai's
resonance. In consequence the orbital decay of highly eccentric orbits is
accelerated. A combination of an axially symmetric gravitational field and
dissipative environment can provide a mechanism explaining the origin of stars
on highly eccentric orbits tightly bound to the central black hole. In the
context of other S-stars, we can conclude that an acceptable mass of the disc
(i.e., M_d<=1 percent of the black hole mass) is compatible with their
surprisingly young age and small pericentre distances, provided these stars
were formed at r<=10^5 gravitational radii.
