Properly prepared (fixed, dehydrated, metal coated) specimens can be stored for a long time in a desiccator. Often for years. Main problem - fungus growth. Clean desiccator and metal coating could supress it.
If stored in buffer? Not long. Without a lipid fixative lipid drift can occur within the specimen. I would say, ...no more than 1 day. In some biologicals, like pig tastebuds, seconds matter between the glut. and OsO4 fixation steps. For single cells a fixative of mixed glut. and OsO4 works nicely. But there is a gradual degradation of the glut/OsO4 blend that takes place over several minutes. So quickness matters. But once fixed, storage life in buffer may be months or even years (if kept microbiologically-clear).
I have even had great success using this fixative blend with more surface-oriented complex cellular structure (like pig taste buds), which are extremely susceptible to lipid drift. Just a thought...