But the nature of what ails him is far from clear. Is it Parkinson's disease, an obstruction of the bowel, or bone cancer? The rumours have been flying for months now, fuelled in part by the intransigence of Vatican officialdom, which until a few days ago was still insisting that nothing was wrong.
So poorly has the issue been handled that the Church now finds itself in the uncomfortable position of having all its pronouncements on the subject routinely disbelieved.
Over the weekend, a few days ahead of the Pope's latest foreign trip, to France, a new announcement sought to shed new light on this darkest of corners in Catholic public relations. All the Pope's health problems, ran a communique from his doctors, were the result of an inflamed appendix which would be removed some time before the end of this year.
Reaction to this news has been as sceptical as ever. Appendicitis does not begin to explain his many symptoms, and an operation to treat it would not normally be deferred. The only concrete part of the communique is that the Pope will go under the surgeon's knife for the sixth time in 15 years, and that sounds distinctly ominous for a man in his condition.
"Maybe he'll soldier on and see in the new millennium as he hopes, but the atmosphere in the Vatican is unmistakably one of fin de regne," one Monsignor told the Rome newspaper La Repubblica last week.
In the absence of reliable bulletins, one can only attempt intelligent guesswork. Parkinson's disease would explain the shaky hands, slightly slurred speech and repeated falls that have caused fractures to the Pope's shoulder blade and hip. And it seems reasonable to suppose some kind of abdominal trouble. The Pope had nearly a yard of intestine removed following the shooting in St Peter's Square that nearly killed him in 1981, and in 1992 surgeons removed a tumour the size of an orange from his bowel.
Last Christmas, the Pope was forced to break off his traditional greetings because of a sudden attack of nausea. In August, another bout of abdominal pain prompted an emergency CAT scan.
What does all this mean? Ten days ago, the Vatican's spokesman, Joaquin Navarro Valls, referred to two "mystery bacteria" that doctors were trying to identify; now the talk is of appendicitis. Such official squirming is not a pretty sight, and does little honour to a Pope who, despite his troubles, still maintains a packed schedule of meetings and foreign trips - one to France this week and three more planned for next year.
n Calcutta (Reuter) - Mother Teresa was rushed to hospital yesterday after suffering a fall at her Missionaries of Charity religious order in Calcutta and hurting her head, hospital officials and an aide said. She was taken to the intensive care cardiac unit at the Woodland Nursing Home, in Calcutta.