Like most stories out of Burma, the recent spate of ethnic cleansing of a Muslim minority sect would be unlikely to receive much Western attention—were it not for Aung San Suu Kyi, the dissident-turned-de-facto-ruler. But unlike in the past, the stories about her are not so flattering now. In fact, they seem directly at odds with the moral leadership that won her the Nobel Peace Prize in 1991.

That prize, and her quiet perseverance (including years of house arrest) against Burma’s ruling military junta, turned Suu Kyi into something resembling a secular saint. Yet now that she has risen to power, and the Burmese state that she leads appears to be overseeing the bloody removal of Rohingya Muslims, her legacy seems different. What happens when a Nobel Peace Prize winner oversees a government committing atrocities?

One thing that will not happen is Suu Kyi losing her prize. The Nobel Foundation’s bylaws state that “No appeals may be made against the decision of a prize-awarding body with regard to the award of a prize.” What has happened, and will likely accelerate, is the tarnishing of her reputation.

Already, some fellow laureates have offered unusual public criticism. Malala Yousafzai (2014) issued a statement pleading with Suu Kyi to condemn the violence. Archbishop Desmond Tutu (1984) wrote a blistering letter to “My dear Aung San Suu Kyi” in which he said that though retired, he felt compelled to break “my vow to remain silent on public affairs out of profound sadness about the plight of the Muslim minority in your country, the Rohingya” and said, “It is incongruous for a symbol of righteousness to lead such a country; it is adding to our pain.”

This week, rather than risk international censure, Suu Kyi decided to skip the UN General Assembly. Yet her immense personal popularity seems to be insulating Burma (and herself) from stronger criticism and a return to the pariah status in which the country long languished—in large part because of its suppression of Suu Kyi’s democratic movement. Her popularity has likely forestalled greater focus on previous rounds of violence directed at the Rohingya, too.

The question of taint on a Nobel Peace laureate is hardly new. Even the most revered winners are not entirely beyond reproach—Mother Teresa (1979), meet Christopher Hitchens—and some of the most famous winners of the prize have been deeply morally compromised even at the time of their victories. One reason for that is that the committee has historically vacillated between awarding prizes for concrete achievements, such as negotiating a specific treaty, and awarding prizes for more symbolic achievements, like Suu Kyi’s, or like Yousafzai’s.

When aimed at concrete achievements, the award is, as Jesse Lansner cleverly puts it, more like naming a most valuable player for a season than it is like inducting someone into the Hall of Fame. Take the 1973 award, given to Henry Kissinger and Le Duc Tho for their roles in ending the Vietnam War. Tho declined the award, deeming it premature, but Kissinger accepted. The German-American statesman is, to put it mildly, a lightning rod for criticism; Hitchens labeled him a war criminal. By the time of the award, Kissinger had helped forestall an earlier peace deal in Vietnam and backed the bombing of Cambodia. He had also encouraged the toppling of Chilean President Salvador Allende in favor of the dictator Augusto Pinochet. And more bad behavior has occurred or come to light since, including condoning genocides in East Timor and what was then East Pakistan and is now Bangladesh. The case for Kissinger’s Nobel (whether one agrees or not) is that even if he was morally compromised, his role in ending a bloody conflict was a great positive for humanity.

Plenty of other winners have major flaws too. Elihu Root (1912) won for his career in diplomacy, despite overseeing the bloody and repressive U.S. occupation of the Philippines. One of the presidents whom he served in implementing that policy, Teddy Roosevelt, was also a laureate, in 1906. Menachem Begin and Anwar Sadat (1978) each had plenty of detractors; Yasser Arafat (1994) had even more. F.W. DeKlerk was a hardline apartheid supporter for years before negotiating the end of the bitter South African regime, for which he won the prize with Nelson Mandela in 1993.

In other cases, the achievement for which someone won the award starts to look less impressive over time. Woodrow Wilson, fervent racist, won with Louis Bourgeois for their creation of the League of Nations in 1919, an accomplishment that with historical hindsight was ephemeral and inadequate. Juan Manuel Santos won the 2016 award the same week that voters rejected the peace deal he’d struck with Colombia’s FARC rebels. (Santos has since successfully revived it.)

Other categories of the Nobel Prizes have their own problems. Science laureates have such a peculiar tendency to fall for quackery after winning—from the Curies’ endorsement of psychics to Linus Pauling’s embrace of Vitamin C as a miracle cure—that it’s been deemed “Nobel disease.”

But the Nobel Peace Prize has its own, special valence, different from the awards for science. A Nobel Prize in chemistry anoints one as an eternal great in the field, but it doesn’t beatify the recipient the way a Peace Prize sometimes seems to do. This is particularly troublesome for those laureates whose prizes seem more symbolic than achievement-based, because there is always the danger that the symbols might start taking material actions.

Put another way, a cynic might say that while Aung San Suu Kyi was an inspiring icon of democratic aspirations when she was sidelined, her great mistake was actually acceding to power. Once she became a leader, she had the opportunity to show that she was a real person with real flaws. As Tutu wrote in his letter, “If the political price of your ascension to the highest office in Myanmar is your silence, the price is surely too steep.”

In retrospect, perhaps her silence on and implicit endorsement of the cleansing of Rohingya should come as less of a surprise. Sectarian violence between Buddhists and Muslims in Burma has raged sporadically for nearly a century. Suu Kyi’s National League for Democracy, while not avowedly a Buddhist or ethnic Burman party, still effectively exists as one. The junta’s decline, and Suu Kyi’s rise, depended heavily on the support of Buddhist monks, as William McGowan wrote in 2012, and various leading members of the NLD have made disparaging statements about Rohingya. “The Rohingya are not our citizens,” a spokesman said in 2012.

It’s hard to find another example of a Nobel Peace laureate endorsing behavior quite so disturbing as what Suu Kyi appears to be endorsing now, but there are other cases of people who, after winning awards, seemed to betray the principles of the prize—though none in such dramatic fashion. Lech Walesa (1993), the Solidarity leader who helped defeat Communism in Poland and later went on to become president, has in recent years drawn unflattering notice for his comments on gay people.

Or take Barack Obama, whose 2009 award appeared to be granted as a symbolic celebration of George W. Bush’s departure from the Oval Office. Obama’s endorsement, in his acceptance speech, of war as a just and proper tool in some situations turned out to be an omen: Though he worked to wind down the American wars in Afghanistan and Iraq, he oversaw the surge in Afghanistan, wars of choice in Libya and Syria, and an expanded drone campaign. Each of these is a defensible choice, but sits uneasily with Alfred Nobel’s description of the peace laureate as “the person who shall have done the most or the best work for fraternity between nations [or] for the abolition or reduction of standing armies.”

Those words are also dramatically less applicable to Aung San Suu Kyi today than they were in 1991, when she received the Nobel. As the cleansing of the Rohingya continues, with only vague and inadequate statements from her, Suu Kyi has much to lose: her moral authority, international adulation, and secular sainthood. Two things she can count on not losing, however, are her Nobel diploma and medal.