Kilz 2 is a latex primer and takes time to fully cure and stick. It can be painted as soon as it dries but will not have full adhesion until it cures, it will cure under the paint.
One possible problem you are experiencing is incompatibility. You didn't mention the type of original paint your painting over, but hard shiny oil base paints need an oil base primer. It has been my experience that the acrylic/latex primers don't stick as well to these surfaces.