With the Middle East being in the current state that it is, it is not surprising that people are looting the antiquities in Iraq. When put in traumatic situations, it is human nature for people to lash out and cause destruction. Also, it is not common for destruction to happen in times of war.
What can/should be done to help save Iraq’s antiquities? Well, there really isn’t a definite answer to that. We could enlist the powers of the UN to help curb the theft, but with no sovereignty, there is nothing that can be done to punish those caught. Iraq’s government is more focused on saving people from the havoc in the streets, rather than saving these pieces of art, which isn’t necessarily a bad thing. The US could help with more security in the Baghdad Art Museum, but that security can only last so long; troops are needed elsewhere in the city to help protect people.
I think that harsher punishments need to be put in place for those caught stealing, but right now, Iraq doesn’t have a stable enough government to do so. It is sad to say, but until the violence calms down a little, not much can be done.