Well, first of all, the adage in the title - it is not the opposite of strength to stop when your actions are proving counterproductive. Rather, the definition of madness is to continue the same actions while expecting different results.
I will first admit that I have no military experience. At best, I have a little experience with some strategic textbook theory and the kinds of mathematical models that one attempts to fit to the madness of the war enterprise. For example, one set of ideas states that if you kill enough of your enemy or destroy enough of the infrastructure, your opposition will fold. In fact, that is one line of reasoning weapons makers take in showing that you can kill X within time period Y, which will shorten your war to Z number of days.
However, the equations of attrition warfare don't quite work for terrorism. One type of equation I found:
dX / dt = -k * X
The above in words is very simple: "The reduction in enemy is equal to the kill rate times the number of enemy." This type of math leads to an exponential decay of the number of people you fight. It also goes into conventional wisdom about fighting - the beginning is hard, and then things get (more or less) progressively easier until you win. But, of course, this is a very simple way of looking at things. Many complications can be added on to this, but I think only a couple of extra terms need to be added in order to make this equation represent what is happening in Iraq (or any insurgent situation).
We modify the equation to this:
dX / dt = -Ke * X + Kk * Kck * X + Ki * Kci * X
Now, you see a problem. Attacking the enemy doesn't just reduce the enemy population, but it can also build it back up. This structure now allows for three outcomes:
1) The original outcome - exponential decrease of enemy until victory
2) Equilibrium - there will be a steady number of enemy for all time
3) Worst-case - the enemy multiplies exponentially until you are driven out
In the equation above, I made up some constants. Kk and Ki represent civilian deaths and injuries that happen during an attack (say, in an urban center when you bomb one house and cause three others to collapse). Kck and Kci represent the "conversion rates," or the rates at which civilian deaths and injuries translate into new enemies. If you are bombing houses in a tribal society, there is a highly likelihood that the killed or injured will be family. That leads to the kind of anger where a brother or nephew or son will take up arms and fight those that did this horrible thing to him.
I think Saddam reduced Kck and Kci a lot through fear and his Stalinist way of doing things. He killed so many (and wiped out whole tribes) that there was too much fear to fight back. Of course, this translates into a steely hatred, to say nothing of the kind of monster it makes of someone that would seriously pursue this strategy.
To the credit of this military, there are several offices and NCO's that have found ways to reduce the number of insurgents without inflaming the local population. They raised goodwill with the communities, helped set up local governance and made pronouncements like "Anytime you disrespect an Iraqi, you aid the enemy" to their units.
Unfortunately, Kck and Kci can also be raised by an element of "you're next," as in civil war. When you see that people are gunning for you because of who you are, and no other circumstances can save you, there is no chance but self-defense. Thus, by allowing Iraq to melt down into civil war, the current administration has made the military's job exponentially more difficult.
This is now a situation where it is going to make more sense to be smart than tough. The Iraqis will have to learn how to govern themselves and secure themselves, which means that our military will have to step into a more and more advisory role. The "over the horizon" plan makes sense in that the Iraqis will start with routine duties, and then only call in the US for more and more extreme situations.
I also don't know if it is possible to teach the militias to operate in a "joint" manner in the same way that the US services now do (overcoming many institutional rivalries along the way) - but it may also be worthwhile to have these guys fight together. They hate each other now, but eventually a Sunni will save a Shi'ite's life. I think that is part of the argument for the unifying effects on Saddam's military during the Iran-Iraq war. That may be a tangent, but it is also something that getting our military to step aside for may enable.
So, that is essentially my grab-bag of ideas. The main point is that business as usual certainly isn't working, and is likely a formula for keeping a very unpleasant status quo around for some time.