  Ultra-luminous X-ray pulsars (ULXPs) provide a unique opportunity to study
super-Eddington accretion. We present the results of a monitoring campaign of
ULXP NGC 7793 P13. Over our four-year monitoring campaign with Swift,
XMM-Newton, and NuSTAR, we measured a continuous spin-up with $\dot P$ ~
-3.8e-11 s/s. The strength of the spin-up is independent of the observed X-ray
flux, indicating that despite a drop in observed flux in 2019, accretion onto
the source has continued at largely similar rates. The source entered an
apparent off-state in early 2020, which might have resulted in a change in the
accretion geometry as no pulsations were found in observations in July and
August 2020. We used the long-term monitoring to update the orbital ephemeris
and the periodicities seen in both the observed optical/UV and X-ray fluxes. We
find that the optical/UV period is very stable over the years, with
$P_\text{UV}$ = 63.75 (+0.17, -0.12) d. The best-fit orbital period determined
from our X-ray timing results is 64.86 +/- 0.19 d, which is almost a day longer
than previously implied, and the X-ray flux period is 65.21+/- 0.15 d, which is
slightly shorter than previously measured. The physical origin of these
different flux periods is currently unknown. We study the hardness ratio to
search for indications of spectral changes. We find that the hardness ratios at
high energies are very stable and not directly correlated with the observed
flux. At lower energies we observe a small hardening with increased flux, which
might indicate increased obscuration through outflows at higher luminosities.
We find that the pulsed fraction is significantly higher at low fluxes. This
seems to imply that the accretion geometry already changed before the source
entered the deep off-state. We discuss possible scenarios to explain this
behavior, which is likely driven by a precessing accretion disk.
