Very short version: if one side of a conflict has shown it can tolerate a certain level of anxiety, casualties, expense, stalemate, etc, then it is possible that it can keep that up indefinitely. Slight increases are not likely to change their response in the short run. A large increase in perceived cost, casualties, or projected duration is needed to demoralize that party. Not only a change in fortunes, but a perception of change can be sufficient discouragement. For example, the public’s surprize in Vietnam that the North Vietnamese could even launch something as formidable as the Tet Offensive was a discouragement, even though we won decisively. The Spanish defeated superior forces in Mesoamerica because the societies had been decimated (sometimes literally) prior to the arrival of the intimidating looking and sounding Spaniards. The Indians believed the forces of gods and nature were arrayed against them.
Nothing but duration is defeating the American effort in OIF at the moment. We hoped to be gone, we don’t like even temporary stalemates, we get discouraged. An alternative view: Baghdad is in stalemate, and there is fatal violence there. Other than that, not much is wrong in Iraq. We had hoped we could persuade the Sunni Arabs to join a coalition – they won’t. Like the Palestinians, they are insisting that they receive all they think they deserve, no compromise. They may persist in this belief until the ground changes. If we leave, the Shia will wipe them out. I hope it doesn’t come to that. (Alternatively, you could blame it on the Shia for being reasonable about everything but Al Sadr. But I suspect even if he were liquidated, the Sunnis would find some other reason not to come aboard.)