We introduce and formalize an under-studied linguistic phenomenon we call Natural Asemantic Variation (NAV) and investigate it in the context of Machine Translation (MT) robustness. Standard MT models are shown to be less robust to rarer, nuanced language forms, and current robustness techniques do not account for this kind of perturbation despite their prevalence in "real world" data. Experiment results provide more insight into the nature of NAV and we demonstrate strategies to improve performance on NAV. We also show that NAV robustness can be transferred across languages and fine that synthetic perturbations can achieve some but not all of the benefits of human-generated NAV data.