  Ultra-hot Jupiters are likely doomed by tidal forces to undergo orbital decay
and eventual disruption by their stars, but the timescale over which this
process unfolds is unknown. We present results from a long-term project to
monitor ultra-hot Jupiters transits. We recovered WASP-12 b's orbital decay
rate of dP/dt = -29.8 +/- 1.6 ms yr-1, in agreement with prior work. Five other
systems initially had promising non-linear transit ephemerides. However, a
closer examination of two -- WASP-19 b and CoRoT-2 b, both with prior tentative
detections -- revealed several independent errors with the literature timing
data; after correction neither planet shows signs of orbital decay. Meanwhile,
a potential decreasing period for TrES-1 b, dP/dt = -16 +/- 5 ms yr-1,
corresponds to a tidal quality factor Q*' = 160 and likely does not result from
orbital decay, if driven by dissipation within the host star. Nominal period
increases in two systems, WASP-121 b and WASP-46 b, rest on a small handful of
points. Only 1/43 planets (WASP-12 b) in our sample is experiencing detectable
orbital decay. For nearly half (20/42) we can rule out dP/dt as high as
observed for WASP-12 b. Thus while many ultra-hot Jupiters could still be
experiencing rapid decay that we cannot yet detect, a sizeable sub-population
of UHJs are decaying at least an order of magnitude more slowly than WASP-12 b.
Our reanalysis of Kepler-1658 b with no new data finds that it remains a
promising orbital decay candidate. Finally, we recommend that the scientific
community take steps to avoid spurious detections through better management of
the multi-decade-spanning datasets needed to search for and study planetary
orbital decay.
