As highpockets has said a file that you are having problems with will help but if you are unable to add a file for copyright reasons then a couple of screenshots is the next best thing.
I am not sure I understand your problem just now, you said that the smaller size cut perfectly but when you made the size larger it cut all the way through the material, I understand you have used a thicker piece of material but maybe it just isn't thick enough for the size you have made the model, if you increase the length & width of the model then you are going to increase the depth it carves to as well.
Have you checked the shape height in the model properties form ? (wrench icon second from left on modelling tab) it should obviously be less than your material thickness. You can alter the height on that form or use the scale z height of model function (5th icon along on modelling tab)
As Michael has already said check the position of your model in the material block as well