CutterHoles and CutterBoxes use the Sketchup Glue_to function and as such require that you have the proper part of your model selected for it to work. The following will help you place them.
Placing a cutter is the same as placing a shelf inside a cabinet. You would need to place the cabinet in edit mode. Sketchup then sees all of the immediate child parts of the cabinet and its glue_to function will work properly.
If you want to place a cutter on a drawer box part, you need to ensure that the drawer box is in edit mode. You can check the outliner to make sure that you have the right component in edit mode as there are many layers to the drawer system. One way to make sure that you have the right part in edit, is to drill down until you have selected the part that you want to place the cutter on. Now back out a level and you will have the right component in edit.
The Sketchup glue_to function is somewhat finicky in that if you try to place it on the edge of a part... it may glue to the wrong face. The best way to place it, is to position it solidly on the face that you want it to stick to. Now, move it to its desired position...and it will always stay on the face that you initially attached it to.