When Henry Kissinger turned 100 this year, Secretary of State Antony J. Blinken toasted him at one birthday celebration in New York, and the C.I.A. director, William J. Burns, did so at another in Washington. There was a reason: Kissinger managed to retain his role as adviser to Washington’s key policymakers a half century after he left office, oftentimes because what he did then was so relevant to the crises of today.

Mr. Kissinger spoke with Mr. Blinken regularly, including as recently as last month, Mr. Blinken said. He had also consulted with previous secretaries of state, including Condoleezza Rice, Hillary Clinton (who took heat for those conversations during her presidential campaign), John Kerry and Mike Pompeo. But he wasn’t some retired coach, reminiscing about the good old days. Instead, he remained the ultimate back-channeller, especially to leaders in China.

In July, Mr. Kissinger secretly flew to China — by private jet, since it’s an arduous flight even if you are not 100 years old — at the specific invitation of Xi Jinping, who called him an “old friend” and, during a lengthy dinner, told him “China and the United States’ relations will forever be linked to the name ‘Kissinger.’”

It was a calculated move. Mr. Xi was making clear that he wanted to move back toward the warmth that surrounded President Richard M. Nixon’s opening to China in the early 1970s, engineered by Mr. Kissinger in secret interchanges and a remarkable, also secret trip to China. And the July visit helped set up Mr. Xi’s summit meeting with President Biden, outside of San Francisco, this month.

On that same trip, Mr. Kissinger was celebrated at the U.S. Embassy, where R. Nicholas Burns, the current U.S. ambassador, lives in a house that Mr. Kissinger helped get constructed when the United States had a representative to China, but full diplomatic recognition had not yet happened.

Mr. Kissinger met with the embassy’s vast staff, talking about what the process of opening the relationship was like — in an era when it seemed inconceivable China would become the world’s second-largest economy.

The Kissinger conversations with secretaries of state and presidents were not only about navigating the downward spiral in relations with Beijing. He was engaged in strategy discussions on Russia, with whom he negotiated SALT I, a major arms-control treaty. He weighed in on artificial intelligence, a passion of his in recent years and a subject he wrote about at length, often with Eric Schmidt, the former Google chief executive who grew close to the former secretary of state.

To Mr. Kissinger’s many critics, this fervor for remaining involved, decades after he could have retired, showed a thirst for power or an effort to burnish his legacy, which he knew was tarnished by charges he forgave massacres, bombings and the deaths of thousands when doing so served his diplomatic purposes.

But the reason his advice was sought out goes to the depth of his experience: When Mr. Kissinger died on Wednesday, Mr. Blinken was headed to Israel in an effort to win a longer pause in a bloody conflict. Mr. Kissinger had flown the same path, in November 1973, exactly 50 years ago, during his famous shuttle diplomacy.