When Steve Ells, CEO of Chipotle Mexican Grill (CMG), stepped down in November from the fast-casual restaurant chain he founded in 1993, he was just the latest in a long line of CEOs who had overstayed their welcome at the expense of their companies.

The decision by Ells—and his board—was guided by the belief that the company needed a turnaround artist to solve Chipotle’s multiple problems. Plagued by food safety failures and organizational miscues, Chipotle saw its customers and stock value decline under Ells’ leadership. The very skills that made Ells so successful as a founder were not compatible with the new exigencies.

It’s a question neatly turned by The Clash’s 1982 song, “Should I stay or should I go?”

I first discussed the idea of a CEO lifecycle a decade ago with Steven S. Reinemund, the past chairman and CEO of PepsiCo (PEP) and then dean of the Wake Forest University School of Business. Steve believed that lifecycle was just five years. He broke it down as follows:

In year one, the new leader gets to know the company, builds trust and relationships, and establishes a loyal coalition. Year two is spent formulating a strategy and achieving maximum consensus. For years three and four, the executive is operating in full swing and the company is responding. By year five, the CEO should be attending to succession and planning a seamless exit strategy.

(By the way, Steve stayed as PepsiCo’s CEO for exactly five years, though was coaxed into staying a sixth at Wake Forest.)

Under this progression, a good CEO can create so much transformational change that at some point he or she is no longer suited or needed there. It becomes a matter of fitness: Talented executives change the workplace in a way that their skills are no longer needed. In a very real way, they created their own expiration date by, ironically enough, being good at what they do.

The example that most captures “expiring” leadership fitness comes from one of the world’s greatest leaders, Winston Churchill. In October 1940, Churchill took power at Britain’s bleakest moment. Britain was reeling from the defeat at Dunkirk and fearing the Nazis would cross the English Channel. The moment called for a leader who could bring Britain’s sparring political parties together and fight with vision and strength. A churlish and unique character, Churchill bravely succeeded where anyone else would have failed.

But by the end of the war in Europe, five years later, Churchill’s Victorian-era ways were out of mode. A one-time reformer, he wasn’t suited for the tidal change he’d created in what was now a war-weary nation. It was not lost on his political opponents, though, who now had the authority (thanks to him) to respond to voter calls for social reforms. When the public went to the polls in July 1945, Churchill lost resoundingly. (Though, he returned briefly in 1951 for reasons many historians refer to as ‘nostalgia.”)

Hard as it is to reconcile, if chief executives successfully develop the competencies of those around them and remake a culture that has grown fallow or turned a troubled company into a high-performing and agile operation, then the next logical step is to leave.

Counter-intuitively, good leaders do themselves out of a job. They make themselves irrelevant. That’s hard to stomach. It’s a gut punch that deflates the fragile human ego. That’s why it’s harder to leave than to stay. Overcoming the natural inclination to cling to a situation where one’s done especially well is a mark of a great executive. Properly timed exits will safeguard the probability that their transformations will live beyond them.

The answer to “should I stay or should I go” depends on whether executives’ talents are—after his or her transformations—still compatible to the organization current needs.

James R. Bailey is a professor of Leadership at the George Washington University School of Business.