  The absence of Type IIP core-collapse supernovae arising from progenitors
above 17 solar masses suggests the existence of another evolutionary path by
which massive stars end their lives. The direct collapse of a stellar core to a
black hole without the production of a bright, explosive transient is expected
to produce a long-lived, dim, red transient known as a failed supernova.
Despite the detection of a number of candidates for disappearing massive stars
in recent years, conclusive observational evidence for failed supernovae
remains elusive. A custom-built pipeline designed for the detection of faint
transients is used to re-analyse 10 years of observations of 231 nearby
galaxies from the PTF/ZTF surveys. This analysis recovers known supernovae, and
yields a number of interesting transients. However, none of these are
consistent with a failed supernova. Through Monte Carlo tests the recovery
efficiency of our pipeline is quantified. By assuming failed supernovae occur
as a Poissonian process with zero detections in the data set, 95 per cent upper
limits to the rate of failed supernovae are calculated as a function of failed
supernova absolute magnitude. We estimate failed supernovae to be less than
0.61, 0.33, 0.26, or 0.23 of the core-collapse SN rate for absolute magnitudes
of $-11$, $-12$, $-13$, and $-14$ respectively. Finally, we show that if they
exist, the Vera C. Rubin Observatory will find 1.7 - 3.7 failed SNe per year
for an absolute bolometric luminosity of $\sim 6 \times 10^{39} \textrm{ erg
s}^{-1}$ out to distances of 33 - 43 Mpc, depending on their assumed spectral
energy distribution.
