Meningitis is inflammation of the meninges, and can be caused by a variety of agents ; bacterial ( usually the most severe form of meningitis), viral,fungi and parasites, so it sort of depends on which organism whether it can remain dormant in the system or not.
Herpes Simplex Virus for instance, can, once in the system, remain latent for many years, and has been associated with meningitis/encephalitis.
For the most part though, I would say that no, the most common agents that cause meningitis are not organisms that can remain dormant within the system.