  We investigate the influence of nuclear spins on the resistance of helical
edge states of two-dimensional topological insulators (2DTIs). Via the
hyperfine interaction, nuclear spins allow electron backscattering, otherwise
forbidden by time reversal symmetry. We identify two backscattering mechanisms,
depending on whether the nuclear spins are ordered or not. Their temperature
dependence is distinct but both give resistance, which increases with the edge
length, decreasing temperature, and increasing strength of the
electron-electron interaction. Overall, we find that the nuclear spins will
typically shut down the conductance of the 2DTI edges at zero temperature.
