Carbon-enhanced metal-poor (CEMP) r/s-stars show surface-abundance distributions characteristic of the so-called intermediate neutron capture process (i-process) of nucleosynthesis. We previously showed that the ingestion of protons in the convective helium-burning region of a low-mass low-metallicity star can explain the surface abundance distribution observed in CEMP r/s stars relatively well. Such an i-process requires detailed reaction network calculations involving hundreds of nuclei for which reaction rates have not yet been determined experimentally. We investigate the nuclear physics uncertainties affecting the i-process during the AGB phase of low-metallicity low-mass stars by propagating the theoretical uncertainties in the radiative neutron capture cross sections, as well as the 13C(a,n)16O reaction rate, and estimating their impact on the surface-abundance distribution. It is found that considering systematic uncertainties on the various nuclear ingredients affecting the radiative neutron capture rates, surface elemental abundances are typically predicted within +/-0.4 dex. The 56 < Z < 59 region of the spectroscopically relevant heavy-s elements of Ba-La-Ce-Pr as well as the r-dominated Eu element remain relatively unaffected by nuclear uncertainties. In contrast, the inclusion of the direct capture contribution impacts the rates in the neutron-rich A~45, 100, 160, and 200 regions, and the i-process production of the Z~45 and 65-70 elements. Uncertainties in the photon strength function also impact the overabundance factors by typically 0.2-0.4 dex. Nuclear level densities tend to affect abundance predictions mainly in the Z=74-79 regions. The uncertainties associated with the neutron-producing reaction 13C(a,n)16O and the unknown beta-decay rates are found to have a low impact on the overall surface enrichment
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