The major argument against term limits is that it takes away the institutional knowledge of governmental bodies.
Governmental bodies have to deal with complex issues. This becomes more and more true as we go higher up into the government. Congress, for example, has to deal with everything from how to reform the tax code to how to improve the health care system. These are things that are very complex and very difficult to understand. Government officials have to spend a great deal of time educating themselves on these issues.
As government officials spend more time in office, they come to be expert on more and more topics. This would not be possible if the officials were all term limited. Just as a person was getting to really understand a topic, they would no longer be able to serve in the Congress. This would mean that unelected groups would have more power. Congressional staff (unelected people who work for members of Congress or for Congressional committees) would be more important because they would know more than the members. The same would be true for lobbyists. Members of Congress would have to look more to these people for information. In this way, term limits would weaken our government officials and reduce our level of democracy.