  Following the coalescence of binary neutron stars, debris from the merger
which remains marginally bound to the central compact remnant will fallback at
late times, feeding a sustained accretion flow. Unbound winds or a wide-angle
jet from this radiatively-inefficient disk may collide with the comparatively
slow dense kilonova ejecta released from an earlier phase. Under the assumption
that such interaction accelerate cosmic rays to ultra-high energies, we
numerically simulate their propagation and interactions through the dynamical
ejecta. The hadronuclear and photo-hadronic processes experienced by particles
produce isotropic high-energy neutrino fluxes, peaking at times $10^{3-4}\,$s,
which we calculate for two sets of parameters. A first set is inspired by the
observations of GW170817. In the second scenario, which we call optimistic,
parameters are chosen so as to optimize the neutrino flux, within the range
allowed by observation and theory. We find that single sources can only be
detected with IceCube-Gen2 for optimistic scenarios and if located within $\sim
4\,$Mpc. The cumulative flux could contribute to $\sim 0.5-10\%$ of the diffuse
flux observed by the IceCube Observatory, depending on the fall-back power and
the cosmic ray composition. The neutrino emission powered by fallback is nearly
isotropic, and can be used for future correlation studies with gravitational
wave signals.
