JOHANNESBURG  The icon is a very old man now. His hair is white, his body frail. Visitors say Nelson Mandela leans heavily on a cane when he walks into his study. He slips off his shoes, lowers himself into a stiff-backed chair and lifts each leg onto a cushioned stool. His wife, Graça, adjusts his feet “so they’re symmetrical, and gives him a peck,” says George Bizos, his old friend and lawyer.

To Mr. Mandela’s left is a small table piled with newspapers in English and Afrikaans, the language of the whites who imprisoned him for 27 years. Family and old comrades sit to his right, where his hearing is better. His memory has weakened, but he still loves to reminisce, bringing out oft-told stories “like polished stones,” as one visitor put it.

“There’s a quietness about him,” said Barbara Masekela, his chief of staff after his release from prison in 1990. “I find myself trying to amuse him, and I feel joyous when he breaks out in laughter.”

Mr. Mandela, perhaps the world’s most beloved statesman and a natural showman, has repeatedly announced his retirement from public life only to appear at a pop concert in his honor or a political rally. But recently, as he canceled engagements, rumors that he was gravely ill swirled so persistently in South Africa that his foundation released a statement saying he was “as well as anyone can expect of someone who is 91 years old.”