Why doesn't a fractured salt crystal stick back together?
You would have to get the two surfaces (or rather their crystallographic axes) together at the atomically perfect original angle to each other. Otherwise no overall (ionic) binding energy will result: Even if the surface is perfectly even, half the ions will be at places where they feel repulsion rather than attraction by the other side.

With polished metal surfaces, this works much better, also because metal atoms are (in "average") more mobile on a surface than ions.

Another point is humidity. Many surfaces, and certainly ionic substances, adsorb a layer of water from the air, practically instantly. It'll take quite a while before that has diffused out again when you press the surfaces against each other.