How can I stop my air drying clay from losing its shape as it dries? I am using air dry clay more precisely Thai clay. 

How to make sure the shape is not disturb while drying? I had made a cornet shape similar to this one:

 

When I left it to dry overnight the shape distorted and formed a base so that the clay could stand up. However, I don't want it form a base as I want it to keep the circle shape. How can I accomplish that?
You could use a support armature to hold up your sculpture while it dries.

I notice, in your photo, there is something that looks pink icing. That might be how that artist hid where the armature was inserted to hold up their sculpture. After the sculpture dried the armature was removed and the hole that was left behind was hidden by the icing.