America cant win simply because it doesnt have the resources and time, or is unwilling, to spend them to secure a nation with a highly factionalised society.
We topple the one guy filling the power-vacuum, then, try and fill it with our pretty small army by occupation standards, coupled with the high factionalisation of the local population, no wonder Iraq is in the state it is in.
America isnt winning not only because of total lack of competent planning and willingness to pay high for it, but most of all because America might think its top-dog of alot of things, but it doesnt hold monopoly on human nature.
If group A wants to kill group B, and you dont hold absolute control over them, then their going to kill each other, regardless of all the fantastical dreams and fantasies you have for the place.
Willpower doesnt win wars or build cities, resources, time and effort do.
The question boils down to this; Who wants the win more?.
An America that invaded for very shakey reasons, without consensus of the entire political structure of the nation, and with pitiful planning and provision for an effective occupation, or the locals who dont have to do much at all to acheive their goals?.
America is occupying a distant country with little to no observable benefits for the country.
The iraqi's are fighting for various reasons, mostly being percieved threats on their way of life, and when people sincerely feel their way of life is threatened, they get very defensive about it.
"There won't be a civil war in Iraq." Well, look what's happening. Did you know that the Bush Administration didn't know there was the Sh'ias and Sunnis? 
Peace, too ideal too unreal 
