The US should protect everyone at home and abroad. However, since it is that person's choice to leave the country and they should understand the risks in doing so, it is important they know their limitations. The US shouldn't be able to mess with a country's sovereignty for instance. If there is something going on that would cause problems is the host country or that violates laws in the host country then the country involved will have to deal with it.
It is an important part of the American fabric to do what we can to help others, and sometimes that means in other parts of the world. We do not withdraw our military when the going gets tough, and civilians who work in these areas should be able to tough it out and keep helping.
No, the U.S. is not obligated to protect citizens who remain in crisis areas of the world. No one appointed the United States as the supreme guardian of the world. However, just because it is not obligated, doesn't mean it shouldn't. The United States has a history of helping people less fortunate than Americans, and it should continue to do that.
Although it's hard to fathom in a world that is shrinking as quickly as ours is, but Americans cannot be everywhere and do everything for all citizens all the time. We have serious problems at home that we need to deal with before trying to go out and play world police. If an American wants to stay in the middle of Syria, there's simply nothing we can realistically do about that.