The potential for neuromorphic computing to provide intrinsic fault tolerance has long been speculated, but the brain's robustness in neuromorphic applications has yet to be demonstrated. Here, we show that a previously described, natively spiking neuromorphic algorithm for solving partial differential equations is intrinsically tolerant to structural perturbations in the form of ablated neurons and dropped spikes. The tolerance band for these perturbations is large: we find that as many as 32 percent of the neurons and up to 90 percent of the spikes may be entirely dropped before a significant degradation in the accuracy results. Furthermore, this robustness is tunable through structural hyperparameters. This work demonstrates that the specific brain-like inspiration behind the algorithm contributes to a significant degree of robustness expected from brain-like neuromorphic algorithms.