We can look at civilian death as a result of wartime action as one clear example. WWII saw about the same numbers of civilians killed by direct military action as military participants who were killed. When you factor in civilian deaths from indirect causes (famine, the elements, etc), it is estimated that WWII saw over twice as many civilian deaths as military deaths. But even if we leave the civilian travesty that was WWII, it is still a given today that some civilians will lose their lives for our convictions that our cause is just. When we bomb, assault, raid, or blockade a locale, we have an effect on civilians. Sometimes our bombs and bullets hit civilians, and sometimes our bombs and blockades destroy or prevent the building of shelters, hospitals, or food supplies. We know that even in a war most consider just, civilians will pay for that conviction.
But civilians can also pay for our convictions in another way. Instead of dying due to an army's actions, civilians can die due to an army's inaction. There are many genocides and humanitarian crises in which the United States did not intervene because they couldn't or didn't justify the action as a whole. Our picking and choosing of which innocent lives to save based on our just war convictions means that we let some people die for those convictions. Furthermore, there can be civilian deaths due to our inactivity in specific situations. In Vietnam we had the problem of the Vietnamese often dodging in and out of Cambodia - a country in which the U.S. was not allowed to go to pursue fighting. Imagine that hostages or civilians across the border faced imminent harm. What would we do? In general, we would refuse to assist them because it would breach our parameters for warfare. Entering Cambodia would be unjust for us because we didn't have sufficient cause to pick a fight with them. There are many circumstances in which an army under just war conditions must not save the innocent for the sake of their convictions.
Just war theory faces the same accusation as pacifism here. The difference is that those who adhere to a just war tend to think that a loss of civilian life can be legitimate in the long run if the loss is unintentional (though many think intentional killings, like the A-bomb were legitimate) and if the loss is as a result of military action that seeks a greater good. Just war adherents also think that a loss of civilian life by withholding force in morally compromised situations provides them with an excuse for allowing civilian deaths, as they seek to maintain their convictions and standards so their war can continue being justified in their eyes.