yeah each time you torque a scew or bolt you are stretching the steel. Think of bending a piece of metal back and forth repeatedly until it breaks. You are on the same principle.
Also, using any screw in a faceplate is only going to suck it in so far against the wood before breaking the heads. (I have this happen all the time installing leaf hinges in hardwood with a powerdriver set on one of the lowest settings) I have even had it happen putting them in with the original cordless screwdriver. Almost as soon as the head contacts the, in my case, leaf of the hinge, *snap! This would be less so with the heavier screws you are using but still be relative to the amount of torque you are applying.
You really need to set them by hand, at least to tighten them and only make them tight don't force it. In this type of application the joint where the shank meets the head is the weakest part. And screws that small are not going to suck the faceplate into the wood.
Another way to go about it, still by hand is not to tighten them as they go in but to put them on the same way you would replace a valve cover or oil pan, etc. alternate tightening so they work together. Even if you only have 3 in your fp still alternate. Otherwise what can happen is the first screw draws the fp in tight but may even suck it a little into the wood then the second screw draws the other side of the fp in but where it sucked in on the other side acts as a fulcrum excerting even more stress on the head of that screw. It may not break right then and there but the stress remains and thus when you add the strain of turning then the resistance of the cutter.....
Also, make sure the pilot hole is just a little deeper than the length of the screw. If it bottoms out in hardwood that can snap the head as well.
Sorry to be so verbose.... I just finished my second cup of coffee and its kicking in.....