  The first peak s-process elements Rb, Sr, Y and Zr in the post-AGB star
Sakurai's object (V4334 Sagittarii) have been proposed to be the result of
i-process nucleosynthesis in a post-AGB very-late thermal pulse event. We
estimate the nuclear physics uncertainties in the i-process model predictions
to determine whether the remaining discrepancies with observations are
significant and point to potential issues with the underlying astrophysical
model. We find that the dominant source in the nuclear physics uncertainties
are predictions of neutron capture rates on unstable neutron rich nuclei, which
can have uncertainties of more than a factor 20 in the band of the i-process.
We use a Monte Carlo variation of 52 neutron capture rates and a 1D multi-zone
post-processing model for the i-process in Sakurai's object to determine the
cumulative effect of these uncertainties on the final elemental abundance
predictions. We find that the nuclear physics uncertainties are large and
comparable to observational errors. Within these uncertainties the model
predictions are consistent with observations. A correlation analysis of the
results of our MC simulations reveals that the strongest impact on the
predicted abundances of Rb, Sr, Y and Zr is made by the uncertainties in the
(n,$\gamma$) reaction rates of $^{85}$Br, $^{86}$Br, $^{87}$Kr, $^{88}$Kr,
$^{89}$Kr, $^{89}$Rb, $^{89}$Sr, and $^{92}$Sr. (abridged)
