  In this paper we address the general applicability of the method pioneered by
\citet{Zhang2012} in which the motion of the compact object can be tracked
using wind X-ray absorption lines. We present the velocity measurements of the
thermal wind lines observed in the X-ray spectrum of a few low-mass X-ray
binaries: GX 13+1, H 1743$-$322, GRO J1655$-$40 and GRS 1915+105. We find that
the variability in the velocity of the wind lines in about all of the sources
is larger than conceivable radial velocity variations of the compact object. GX
13+1 provides a potential exception, although it would require the red giant
star to be massive with a mass of $\approx 5-6\ M_{\odot}$. We conclude that
the variability of the source luminosity occurring on a time scale of
days/months can affect the outflow properties making it difficult to track the
orbital motion of the compact object using current observations. Given the
intrinsic variability of the outflows we suggest that low-mass X-ray binaries
showing stable coronae instead of an outflow (e.g. 4U 1254$-$69, MXB 1659$-$29,
4U 1624$-$49) could be more suitable targets for tracking the orbital motion of
the compact object.
