The outstanding transport properties expected at the edge of two-dimensional time-reversal invariant topological insulators have proven to be challenging to realize experimentally, and have so far only been demonstrated in very short devices. In search for an explanation to this puzzling observation, here we report a full first-principles calculation of topologically protected transport at the edge of novel quantum spin Hall insulators-specifically, bismuth and antimony halides-based on the nonequilibrium Green's functions formalism. Our calculations unravel two different scattering mechanisms that may affect two-dimensional topological insulators, namely, time-reversal symmetry breaking at vacancy defects and inter-edge scattering mediated by multiple cooperating impurities, possibly nonmagnetic. We discuss their drastic consequences for typical nonlocal transport measurements as well as strategies to mitigate their negative impact. Finally, we provide an instructive comparison of the transport properties of topologically protected edge states to those of the trivial edge states in MoS2 ribbons. Although we focus on a few specific cases (in terms of materials and defect types), our results should be representative for the general case and thus have significance beyond the systems studied here.