What's Wrong with Leaders' Serving More Than Two Terms

Last week, Jack sent me this piece, announcing that Russia's Duma had failed by a wide margin to approve a constitutional change that would allow Vladimir Putin to serve an additional term in office.

A proposed amendment to the Russian Constitution [text in English] that would have allowed President Vladimir Putin [official website] to serve a third term [JURIST report] fell far short of approval by the State Duma on Wednesday. Only 32 members of Russia's lower house voted for it, with 99 voting against. The measure needed 226 votes to pass. Putin's term expires in 2008...

Even though I was raised to believe that term limitations on presidents are a good thing, I am increasingly unconvinced that they are. What is wrong with having a president serve more than two consecutive terms? What is wrong with a lengthy dynasty? Was the United States harmed by having FDR in office for nearly 4 terms?

I don't see anything wrong with it, with two exceptions:

1. Possibly the incumbent has too great an advantage over a challenger. The advantage might be "unfair" control over the access to publicity or over the voting mechanism, or it might simply be brand recognition. Getting rid of political contribution limitations would help deal with this problem.
2. If it's some friggin' elitist interventionist, I'd shudder at the thought that the people might elect the person for a third term.