From what I've gathered both from experience and research, there isn't actually a limit (although nobody has attempted to bury a sphere in every tile).
However, some players noticed that buried spheres may disappear in Diamond/Pearl if they've buried a great deal of them. As far as this goes I can't find anything on an actual limit, as it just seems to be random after you've buried enough, much like traps disappearing.
But since you're playing Platinum this shouldn't be a problem anyway.
Bury to your heart's content!