  In the mHz gravitational-wave band, galactic ultra-compact binaries (UCBs)
are continuous sources emitting at near-constant frequency. The signals from
many of these galactic binaries will be sufficiently strong to be detectable by
the \emph{Laser Interferometer Space Antenna} (LISA) after
${\sim}\mathcal{O}(1\ \text{week})$ of observing. In addition to their
astrophysical value, these UCBs can be used to monitor the data quality of the
observatory. This paper demonstrates the capabilities of galactic UCBs to be
used as calibration sources for LISA by demanding signal coherence between
adjacent week-long data segments separated by a gap in time of \emph{a priori}
unknown duration. A parameter for the gap duration is added to the UCB waveform
model and used in a Markov-chain Monte Carlo algorithm simultaneously fitting
for the astrophysical source parameters. Results from measurements of several
UCBs are combined to produce a joint posterior on the gap duration. The
measurement accuracy's dependence on how much is known about the UCBs through
prior observing, and seasonal variations due to the LISA orbital motion, is
quantified. The duration of data gaps in a two-week segment of data can be
constrained to within \stmo\ using {$\mathcal{O}(10)$} UCBs after one month of
observing. The timing accuracy from UCBs improves to \styr\ after 1 year of
mission operations. These results are robust to within a factor of ${\sim}2$
when taking into account seasonal variations.
