As it dries, the moisture in it goes away and causes some shrinkage. If you added new to partially dry clay, then the oldest piece keeps drying and shrinking, faster than the new piece does. The two pieces are shrinking away from each other.
I don't know what the liquid is in that air dry clay, but I assume it is something that evaporates.
When working with ceramics you can't add wet pieces to dry pieces for the same reason, but you can add water to scraps of clay to create what's called 'slip', just wet gooey clay, but it acts like a glue and will usually hold new clay to leather dry pieces, but not to completely dry pieces.
To do that, you have to rough up the two pieces you are adding together, sort of scratch them in the areas they will connect, then add the slip to both pieces so it bonds them together.
I suspect with air dry clay, it needs to all be made at the same time, so that all the parts dry at the same time. Might help though if you scratch the parts that are to be bonded then push them together well.
Make sense??
