Maybe it’s the peanut butter ice cream he still enjoys. Or the fact that his first-place Atlanta Braves are cruising toward the playoffs and he wants to see another World Series. Or as many of his loved ones and former advisers suggest, maybe he is just too stubborn to follow anyone else’s timetable.

Whatever the reason, seven months after entering hospice care, Jimmy Carter is still hanging on, thank you very much, and is in fact heading toward his 99th birthday in just over a week. While nearly everyone, including his family, assumed that the end was imminent when he gave up full-scale medical care last winter, the farmer-turned-president has once again defied expectations.

“We thought at the beginning of this process that it was going to be in five or so days,” Jason Carter, his grandson, said in an interview, recalling the former president’s decision to check out of the hospital and go into hospice care at his home in Plains, Ga., last February. “I was down there with him in the hospital and then said goodbye. And then we thought it was going to be in that week that it was coming to the end. And it’s just now been seven months.”

Mr. Carter was already the longest-living president in American history, but his staying power even in hospice has captured the imagination of many admirers around the world. It has generated an extended farewell, one that was unplanned yet remarkably affectionate for a president who was turned out of power by voters after a single term yet transformed his legacy with decades of service that earned him the Nobel Peace Prize.

In the months since he returned to his small-town home to meet his final fate, the outpouring of remembrances has been heartening to his family and friends. Instead of a memorial service he could not attend, Mr. Carter has experienced a living eulogy, soaking up tributes from around the globe. Relatives and advisers say he is aware of what has been written and said, and is deeply grateful.

“He’s got so much joy in seeing his presidency and post-presidency revisited,” said Paige Alexander, the chief executive of the Carter Center, the nonprofit institution that served as the base for his philanthropic work over the last four decades. “In many ways, that keeps him going — along with peanut butter ice cream.”

Mr. Carter has withdrawn from the active life he led until not that long ago. The regular calls with Ms. Alexander are no longer so regular. What animated him for so long were not the ins and outs of the daily news but the projects he devoted his life to, like eradicating certain diseases from developing countries.

“He wasn’t asking about politics or the economy,” Ms. Alexander recalled. “He just wanted to know what the Guinea worm count was.” While Mr. Carter has good days and bad days, he has not lost his perspicacity or his sometimes curmudgeonly sense of humor. Ms. Alexander recalled a telephone conversation over the summer when she mentioned his upcoming big day.

“If I don’t talk to you before your birthday, happy birthday,” she recalled telling him.

“I’m going to be 99,” he replied. “I’m not sure what’s so happy about that.”

Nonetheless, the Carter family, both those who are blood relations and those who are part of his longtime circle, are planning various celebrations to mark his century-minus-one milestone on Oct. 1.

The Carter Center is asking supporters to send pictures or videos that will be arranged in a digital mosaic. It collected 6,000 in the first three days, from celebrities like Martin Sheen and Jeff Daniels as well as everyday people from Africa and around the world. Peter Gabriel led an audience in a round of “Happy Birthday, Jimmy” at Madison Square Garden on Monday night.

The next night, the Bill and Melinda Gates Foundation presented its lifetime achievement award to Mr. Carter and his wife, Rosalynn Carter, with Ms. Alexander collecting on their behalf. The Jimmy Carter Presidential Library and Museum will hold a naturalization swearing-in ceremony for new American citizens on his birthday. David Osborne, known as the “pianist to the presidents,” will perform at Mr. Carter’s Maranatha Baptist Church. Mr. Carter was not suffering any particular ailment that prompted him to enter hospice care last February, according to people close to him, but was tired of being in and out of the hospital and wanted to spend his final days at home with Mrs. Carter. Hospice is defined as care for terminally ill patients when the priority is not to provide further treatment but to reduce pain and discomfort toward the end of life. It is meant for patients not expected to live more than six months.

Perhaps it should have been no surprise that Mr. Carter would ignore that time frame. He has been defying death longer than anyone who ever served in the Oval Office. In 2015, he beat cancer that had spread to his brain. In 2019, he bounced back from several falls, including one that broke a hip. “He’s been faced with what he thought was the end multiple times,” Jason Carter said.

He spends his days now in the house where he and Mrs. Carter have lived since 1961, a two-bedroom, one-story rambler so plain that The Washington Post once calculated that it was worth less than the Secret Service vehicles parked out front. His children and grandchildren take turns visiting with them, and he has a crew of caregivers but has not seen a doctor in more than six months.

“It’s a day-to-day thing,” said Kim Fuller, his niece. The children sometimes read him news articles, and he catches Braves games on television. “They holler at the TV and do everything you do normally when you’re watching baseball,” Ms. Fuller said.

Mr. Carter can no longer teach Sunday school at Maranatha as he did for so many years — the church’s website says almost optimistically that he will not be teaching “until further notice” — so Ms. Fuller has taken over.

Her uncle watches her every Sunday on a live Facebook feed. At first, he would offer critiques. “He would let me know if I had said something that wasn’t quite the way it should be,” she said. “He doesn’t anymore. I kind of miss that. I would like for him to.”

Mrs. Carter, the genteel former first lady who made promoting mental health a cause while in the White House, announced in May that she had dementia, and the two of them spend days together quietly. “She’s very happy,” Jason Carter said. “She’s reminiscing and remembering some of the great times she’s had.” As Ms. Alexander put it, “They continue to offer us lessons in dignity and grace.”

For Mrs. Carter’s 96th birthday last month, Ms. Fuller said she organized a butterfly release at the house. Ms. Fuller said her uncle was aware of his own upcoming birthday.

“He wants to reach 99, I know that,” she said. “The last month has been different for him,” she added, but “I am just praying every day that he makes it to 99.”

“It’s a bittersweet one,” she added. “We’ve all been on pins and needles since February. Every day’s a celebration.” But as her uncle has demonstrated time and again for nearly a century, no one will dictate to him. “He’s going to do exactly what he wants to do when he wants to do it.”

For Mr. Carter, any birthday celebration will be marked at home, surrounded by family.

“He’s really significantly limited physically and he is coming to the end, there’s no doubt about that,” Jason Carter said. “He is, I think, frustrated by that. But he is at home. He’s together with his wife. They’re in love. They’re at peace and you don’t get more from that. You certainly don’t get more than they got from this life. And the end is exactly how you would hope for it to be.”