It is a particularly modern dilemma, tied to a time when the demands on these men have expanded exponentially since their faiths began. They live ever longer and lead even more publicly. They are expected to travel widely, to preach and teach thousands, if not millions, and to do it all under the glare of media scrutiny. Followers crave charismatic figures who can charm reporters and believers alike, who can speak with moral authority and who can transcend the vicissitudes of mortal aging.
For the 85-year-old Benedict, the answer was clear: It couldn't be done.
"Three or four centuries ago, if the pope got really sick or went nuts, you'd put him a backroom and the church kept moving along," says the Rev. Thomas Reese, a Jesuit priest and senior fellow at Georgetown University's Woodstock Theological Center. "We have had a couple of crazy popes that caused schisms I'm thinking of the [medieval] Borgias but we can't poison them anymore."
Today's church "is a global village," Reese says. "It is a much more difficult problem."
And not just for the world's billion Catholics.
Now several faiths also might consider whether to maintain the no-exit clause for their chief hierarchs or to allow them to step aside when declining health makes it almost impossible to continue. What would such an early departure do to the system that propelled these men to their positions in the first place? Would the dynamic between leader and disciples change? Would it diminish the reverence for and holiness of their role?
These are "extraordinary times," says Massimo Introvigne, chair of the Italian Observatory on Religious Liberty, which call for "extraordinary decisions."
"On the one hand, the idea of a lifetime calling is part of the mystique accompanying certain special sacred positions, such as pope, Dalai Lama or Mormon prophet," Introvigne writes in an email. "On the other hand, they preside over increasingly complicated organizations."
Perhaps no church structure, he says, is "more complicated than the Catholic Church."
Shoes of the fisherman • Catholics believe that Jesus picked Peter, the Galilean disciple, to lead his church and that every pope, which means "father," has been chosen to protect and pass on the faith.
He is selected by a two-thirds vote of the College of Cardinals. When a pontiff dies, the cardinals retire to a sequestered section in the Vatican and remain there until a leader has been elected. The conclave's votes are cast on paper. After each round, those ballots are burned. Black smoke billowing from a chimney overlooking St. Peter's Square means no pope has been elected; white smoke means one has.
Though popes are often beloved to the believers, Reese says Catholics revere the office, not the officeholder.
Traditionally, a pope did not resign because his role was that of a "father," he says. "You can't resign from paternity. A father of a family is there until he dies. No one else can pick up that role."
But a pontiff is also bishop of a global community, which means he is akin to a political leader and head of a huge bureaucracy.
Benedict's predecessor, the internationally popular John Paul II, could run across the stage and across the world when he was elevated to pope, Reese says. "At the end, we saw him as an infirm old man who could hardly talk."
To the Catholic scholar, Benedict's resignation was "inevitable."
"The pope recognized he wasn't up to the task," Reese says. "God was telling him through his illness that it was time to step aside."
With Benedict leaving, the church faces a bevy of questions: What do you do with an ex-pope? What do you call him? If he writes anything and Benedict is a prolific author and theologian the media will look for any area of disagreement with the new pope. And, in the future, people may pressure a pope to resign not because he is ill, but because they don't like him.
"This," Reese says, "will all have to be played very carefully."
The prophetic mantle • Mormonism was founded in 1830 by Joseph Smith, an upstate New York farm boy who said God told him to restore Christianity as it was originally. He also said he translated an ancient history written on gold plates, which were buried in the ground and became the religion's signature scripture, the Book of Mormon.
Smith's mystical experiences, revelatory claims and charismatic leadership launched a movement that, like many others, faced severe succession conflicts when he died (a mob murdered Smith in 1844 in Illinois). Ultimately, for most Latter-day Saints, the baton was passed to Brigham Young, the senior member of Smith's handpicked Quorum of Twelve Apostles.
The pattern eventually became for the longest-serving apostle to ascend to the church's highest office: the president, who is considered a "prophet, seer and revelator" to the Utah-based faith's 14 million members. He chooses two men to serve as his counselors in a three-man First Presidency.
But Smith's apostles were relatively young men. Young was 43 when his predecessor perished; he lived to be 76, spending nearly 30 years as church president.
Since then, medical improvements and healthy lifestyles have allowed LDS leaders to live long into their 80s and 90s. Like John Paul and Benedict, some Mormon presidents especially in the latter 20th century have had to deal with the afflictions of aging. David O. McKay, Spencer W. Kimball, Joseph Fielding Smith and Ezra Taft Benson all largely retired from public view in their final years, leaving the running of a growing global church to healthier counselors in the governing First Presidency (which itself can be expanded to include additional counselors).
To cope with aging at lower LDS leadership levels, some of the older members of the Seventy were "retired" or given emeritus status in 1978. Eventually, it became the norm for the Seventy to retire at 70.
No such system is in place for apostles, who are all seen as "prophets, seers and revelators" and are on an inexorable climb to the church's presidency.
"We don't make apostles retire because we think God is working through mortality tables," says LDS historian Richard Bushman, an emeritus professor at Columbia University. "It would be going against God."
Plus, he says, "an incapacitated president is less of a problem in our church because of the counselors. If the president can't do the job, everyone knows who is next in charge. He can take over and everyone respects his authority."
The current LDS president, Thomas S. Monson, is a few months younger than the pope. He has continued to travel, though not as frequently as he did in the first months of his presidency, which began in February 2008. He still speaks at services, including funerals, and at twice-yearly General Conferences.
"Last August I celebrated my 85th birthday. Some of the senior members of the Quorum of the Twelve have a few years even on me. Age eventually takes its toll on all of us," the Mormon prophet wrote in a letter to members marking his five years in the job. "Despite any health challenges that may come to us, despite any weakness in body or mind, we serve to the best of our ability. I assure you that the church is in good hands."
If Monson's health took a turn, his counselors no doubt would do much of the work along with the other 12 apostles as has been the practice in the past.
Some members point to the Book of Mormon, where prophets often handed over their office to younger men. Others look at a passage in the LDS Doctrine & Covenants that could, hypothetically, make it possible for a church president to step aside, but only if interpreted in a certain way. Section 43, verse 4 says: "But verily, verily, I say unto you, that none else shall be appointed unto this gift [to receive divine revelation] except it be through him [church president]; for if it be taken from him he shall not have power except to appoint another in his stead."
If a Mormon prophet felt his mental and physical capacities were so compromised that he no longer could fulfill the obligations of his office, he potentially could turn over the job to his expected successor: the senior apostle.
"That would be in harmony with that passage," Bushman says, "and I think Mormons would feel comfortable."
Any other option would be "such a reversal of our customary procedures that the whole system would be undermined," the historian says. "It was would be scary for the Saints to tamper with it."
The LDS succession system protects the church from "politicking and factionalism," says American religion historian Kathleen Flake of Vanderbilt University in Nashville, Tenn. "There's no way to move ahead in the line by your own effort, so everyone relaxes and does the job."
The system provides security and predictability, she says. "Though counselors can't replace the president, they can make the trains run and reflect the charismatic authority of the prophet."
The only downside is that during periods when the counselors are carrying the bulk of responsibilities for a declining leader, she says, long-range goals of the institution go unattended.
Mormonism has "romanticized the office of the prophet," she says, "which makes it difficult to see how it operates on a practical level."
Buddha incarnate • Buddhists believe that a sixth-century Indian prince named Siddhartha Gautama left his palace, wandered in the wilderness for a half dozen years and found enlightenment while sitting under a Bodhi tree. Among other teachings, the Buddha preached that each person goes through a continual cycle of incarnations, gaining wisdom and compassion with each life until he or she attains an enlightened state.
That soul, then, is free.
Tibetan Buddhists, though, believe that some souls choose to return even after their enlightenment to be an example to others. Among these are the dalai lamas. A reincarnated dalai lama is recognized early, sometimes as a young child of 7 or 8, and thus lives out his life as "the embodiment of Buddha."
His is not an office nor a clear-cut set of tasks. Though he does have attendants and major responsibilities, today's Dalai Lama does not supervise a big bureaucracy. The 77-year-old does not appoint the leaders of a monastery nor set the rules for meditation or worship.
"To practitioners, His Holiness the Dalai Lama is the spiritual embodiment of the Buddha of Compassion that encompasses all the enlightenment of past and present," says Jerry Gardner, also known as Lama Thupten, spiritual leader at Urgyen Samten Ling, Salt Lake City's Tibetan Buddhist Temple. "If His Holiness was to have some mental illness or physical illness, that wouldn't negate the innate qualities that are primordial to his enlightened mind."
There are many stories of great Tibetan Buddhist masters from the past "who, in an ordinary, mundane sense, may be viewed as being incapable of functioning," Gardner says, "but they are still able to exhibit those qualities."
Gardner explains it this way: If you have a piece of gold and then someone drops it into a pile of garbage, a mud pit or a cesspool, it may become encased in the muck. We no longer see the gold, but it's still there.
That's how Tibetans view their leader: No matter his physical or mental condition, the gold is still there.
For centuries, though, the Dalai Lama was also the political leader of Tibet, as well as the spiritual head of Tibetans in exile. He recently relinquished his political role and, because of China's control of the former Buddhist nation, has said his next incarnation would likely not come from Tibet.
"His Holiness is a scholar and deep practitioner," says Jean LaSarre Gardner, Jerry Gardner's wife and fellow Buddhist. "He calls himself a simple monk. That's how he views himself."
It is the people who give him reverence and elevate him into a form of devotion, she says. "That is not something he or his position asks for," Jean Gardner says. "If he became incapacitated physically, that wouldn't matter at all."
When he passes, she says, "we would still see him as the Dalai Lama."
And that may be one of the big questions facing Catholics in coming months: Will they still see Benedict as the pope?