I don't really know anything about Cayce School. I'm guessing that given the name, it was the school in Cayce at one time. The (Guignard?) brick architecture could easily go back to the 1940s I suppose. The pictures don't really make it clear, but as this aerial view from google maps shows, the school is really just one building with several different wings:
Of course it's a building that takes up a block of its own, being bounded by 3rd Avenue, Lexington Avenue (on which it fronts), Poplar Street and 8th Street.
At some point it appears that it stopped being a "school" as such and was taken over by Lexington District Two as a "Learning Center". (I have to say that the picture with the sign indicating such would make a good funny email to forward around Mississippi education circles..).
The building has obviously been out of use for a good while, and I think only the fact that it is in the middle of a residential area has kept it from being vandalized and tagged to a fare-thee-well. Certainly it is decrepit, which can be seen in the google view (which can be zoomed) as well as my pictures. Signs around the school indicate that the lot is to become luxury townhomes in a gated community, so I suppose the building will be demolished at some point, though with the current real-estate market, I doubt the developers will be in a big hurry.
(Hat tip to commenter tonkatoy)
UPDATE 23 July 2011 -- Adding the entire 26 June 2011 photoset below.