Such is the position of Rambam, in Mishneh Torah, Hilchos Sanhedrin 2:3:
אין מעמידין בכל סנהדרין לא זקן מופלג בשנים ולא סריס, מפני שיש בהן אכזרייות.
Other reasons for this halachah can be added. As I once wrote in a post entitled Strength in Leadership, leaders must have a certain degree of vigor, in order to be able to be in control, and to be perceived that way. In the post, I speculated that the current problems of weakness in charedi leadership are a result of modern medicine prolonging the lives of people who lack the strength to lead.
It turns out that in the wake of the Pope's resignation, others are making the same point:
Joseph Curran, professor of religious studies at Misericordia University in Dallas, Pennsylvania, said the modern medicine prolonging the life of people had posed difficulties for institutions whose leaders usually rule for life.It's good that the pope recognizes this. Apparently, papal infallibility helps him realize that he is all too fallible.
"His resignation is a tremendous act of humility and generosity," he said. "A man who lives up a position of authority because he can no longer adequately exercise that authority, and does so for the good of the Church, is setting a wonderful example," he said.
This in turn reminds me of an interesting observation that someone once made. Charedi Judaism does not claim infallibility for its leaders, but in practice never admits to their being wrong. The church, on the other hand, does claim infallibility for its leaders, but in practice they have shown themselves ready to admit being wrong!
(Hat tip: Michapeset)