The ocular motor system provides several advantages for studying the brain, including well-defined populations of neurons that contribute to specific eye movements. Generation of rapid eye movements (saccades) depends on excitatory burst neurons (EBN) and omnipause neurons (OPN) within the brainstem, both types of cells are highly active. Experimental lesions of EBN and OPN cause slowing or complete loss of saccades. We report a patient who developed a permanent, selective saccadic palsy following cardiac surgery. When she died several years later, surprisingly, autopsy showed preservation of EBN and OPN. We therefore considered other mechanisms that could explain her saccadic palsy. Recent work has shown that both EBN and OPN are ensheathed by perineuronal nets (PN), which are specialized extracellular matrix structures that may help stabilize synaptic contacts, promote local ion homeostasis, or play a protective role in certain highly active neurons. Here, we review the possibility that damage to PN, rather than to the neurons they support, could lead to neuronal dysfunction-such as saccadic palsy. We also suggest how future studies could test this hypothesis, which may provide insights into the vulnerability of other active neurons in the nervous system that depend on PN.