  The ultra-luminous intermediate-mass black-hole system HLX-1 in the ESO
243-49 galaxy exhibits variability with a possible recurrence time of a few
hundred days. Finding the origin of this variability would constrain the still
largely unknown properties of this extraordinary object. Since it exhibits an
intensity-hardness behavior characteristic of black-hole X-ray transients, we
have analyzed the variability of HLX-1 in the framework of the disk instability
model that explains outbursts of such systems. We find that the long-term
variability of HLX-1 is unlikely to be explained by a model in which outbursts
are triggered by thermal-viscous instabilities in an accretion disc. Possible
alternatives include the instability in a radiation-pressure dominated disk but
we argue that a more likely explanation is a modulated mass-transfer due to
tidal stripping of a star on an eccentric orbit around the intermediate-mass
black hole. We consider an evolutionary scenario leading to the creation of
such a system and estimate the probability of its observation. We conclude,
using a simplified dynamical model of the post-collapse cluster, that no more
than 1/100 to 1/10 of Mbh < 10^4 Msun IMBHs - formed by run-away stellar
mergers in the dense collapsed cores of young clusters - could have a few times
1 Msun Main-Sequence star evolve to an AGB on an orbit eccentric enough for
mass transfer at periapse, while avoiding collisional destruction or being
scattered into the IMBH by 2-body encounters. The finite but low probability of
this configuration is consistent with the uniqueness of HLX-1. We note,
however, that the actual response of a standard accretion disk to bursts of
mass transfer may be too slow to explain the observations unless the orbit is
close to parabolic (and hence even rarer) and/or additional heating, presumably
linked to the highly time-dependent gravitational potential, are invoked.
