Fixing cracks in air-dried clay?
My experience so far is that cheaper air-drying clays tend to shrink more than quality clays while drying. Many types of clay list the expected shrinkage on the package. If there is no information about shrinkage, you should expect it to be non-negligible (sometimes as much as 10%). As far as I understand it, different fibres added to the clay are to blame. Cheap clays use fibres that soak up more water because you pay by weight. More water in the clay means less expensive ingredients by weight.

"Super soft" and "super light" clays are also full of fibres. I would always prefer a clay with the texture and consistency of natural clay. 

Slowing the drying process down is a very good idea. If the outer layer of clay dries and shrinks faster than the inner layer, it cannot shrink uniformly and has to crack. If there are badly mended cracks in the soft clay, they tend to reopen while drying.

The thickness of the clay may have an effect as well. When you form very thick structures like a fist-sized ball, you should substitute part of the clay with another material like a ball of aluminium foil.

When your sculpture cracks, you should moisten the cracked area, fill it in with fresh clay and really rub it into the crack to attach it to the dried clay. If the fresh clay won't stick at all, it's a sign of bad quality clay.