There is, of course, no consensus among scholars of International Relations on this issue. Realists certainly do not believe that their theories are becoming outdated. Let us look at arguments both for and against the proposition that realism has outlived its usefulness.
The major argument for this idea has to do with the idea that the primacy of the state as an actor in international affairs is disappearing. One of the main tenets of realism is the idea that the only states truly matter in the international arena. It is easy to argue that this is no longer even remotely true. After all, American foreign policy for the last 12 years or so (since 9/11/2001) has been driven in very important ways by our need to protect ourselves against Al Qaeda terrorism. If Al Qaeda, which is not a state, can have such an impact on international affairs in the modern world, realism would seem to be outdated.
A second argument has to do with the idea that states always have a unitary interest in security and always act according to those interests. In this view, things like changes in government do not matter. States have interests that exist whether their government is democratic or autocratic and they will pursue those goals in the same way regardless of the type of government they have. Events like the Arab Spring seem to put the lie to this. It appears that, for example, Egypt’s foreign policies will be very different under military rule than under Islamist rule. This, too, seems to make realism outdated.
Realists, on the other hand, would still argue that their theories are applicable. They might argue that Al Qaeda is not a true threat to the United States. That is, there is no way that Al Qaeda could threaten the entire existence of our country. Instead, they would argue that the gravest threats to the United States come from states like China. They would point to issues that are arising as China becomes more powerful. They would say that China is trying to make itself more secure by trying to dominate its region. They would say that this threatens us and makes us seem less secure (the security dilemma). They would say that a war with China would be much more damaging to the US than any number of Al Qaeda attacks.
There is, then, no objectively correct answer to this question. I tend to think that realism is outdated, but I never did buy into realism completely, even in the days of the Cold War. In other words, that is my own biased opinion and other people could think differently.