  We present the results of an investigation of a highly variable CIV broad
absorption-line feature in the quasar SBS 1408+544 (z=2.337) that shows a
significant shift in velocity over time. This source was observed as a part of
the Sloan Digital Sky Survey Reverberation Mapping Project and the SDSS-V Black
Hole Mapper Reverberation Mapping Project, and has been included in two
previous studies, both of which identified significant variability in a
high-velocity CIV broad absorption line (BAL) on timescales of just a few days
in the quasar rest frame. Using ~130 spectra acquired over eight years of
spectroscopic monitoring with SDSS, we have determined that this BAL is not
only varying in strength, but is also systematically shifting to higher
velocities. Using cross-correlation methods, we measure the velocity shifts
(and corresponding acceleration) of the BAL on a wide range of timescales,
measuring an overall velocity shift of delta v = -683 (+89, -84) km s-1 over
the 8-year monitoring period. This corresponds to an average rest-frame
acceleration of a=1.04 (+0.14, -0.13) cm s-2, though the magnitude of the
acceleration on shorter timescales is not constant throughout. We place our
measurements in the context of BAL-acceleration models and examine various
possible causes of the observed velocity shift.
