--AKA "everybody's virus" in that at least 95% of us have been infected by age 35 and will show certain antibody titres to it for life (like all the human herpes family viruses, EBV is not eradicated, but held in check by a proper immune system, generally lying dormant in the nasopharynx unless "reactivated" in times of immune compromise), has been implicated in some neuropathies, both in initial infection and reactivation scenarios.
The mechanism is thought to be molecular mimicry (which is thought to be behind a lot of autoimmune reactions); the pathogen has a shape very similar to some bodily tissue, and since much of the immune antibody reaction in done by shape--think key in lock--an immune system activated by such a pathogen may attack anything with a similar shape, including actual body tissue.
Viruses are not the only culprits here; there is strong evidence for certain neuropathies, particularly acute ones such as Guillain Barre, having a bacterial "infectious prodrome". In the case of Guillain Barre, a number of cases are known to have followed infection by Campylobacter jejuni and Haemophilus influenzae.
See:
http://neuromuscular.wustl.edu/antibody/gbs.htm
http://neuromuscular.wustl.edu/nother/infect.htm
http://neuromuscular.wustl.edu/senso...html#sfpnacute