Why doesn't graphite dissolve in organic solvent?
While you cannot directly make a suspension or dispersion of graphene nano-platelets from graphite, it is possible to perform very similar process, called exfoliation, on graphite oxide, as graphite oxide has functional groups decorating it that reduce the functional strength of the van der Waal's forces between layers.
The exfoliation process can create a dispersion of graphene nanoplatelets in an organic environment, however, outside energy is often (if not always) necessary to promote the exfoliation of the individual layers. Most often, this energy is provided by sonicating the solution.
A very quick search of suggests that this method has been shown to work using NMP, DMF, THF, and ethelyne glycol. (see Paredes, Villar-Rodil, Martínez-Alonso, and Tascón, 2008 for more info)