Shortly before Hillary Clinton told a cheering Kentucky crowd in the Louisville Marriott Hotel that she never gives in, her relentlessly upbeat campaign chairman Terry McAuliffe was asked if he had talked to her about dropping out.

Amid hundreds of women waving signs such as “Overy Vote Matters!” and “You Go Girl!”, Mr McAuliffe said: “I don’t have those discussions with Hillary Clinton. If you know Hillary Clinton — and myself — we don’t believe in losing.” In truth, in recent days some friends and fundraisers have tentatively suggested to the former First Lady that her insistence on staying in the Democratic race, against overwhelming odds, threatens to split the party along race and gender lines and risks damaging Barack Obama’s chances against John McCain.

They have been given short shrift. Inside her campaign there are aides who believe in their hearts that it is all over. Recriminations have already begun. Mrs Clinton knows her chances are slim, yet she is more determined than ever to press on. She will not countenance talk of quitting. Just what is she thinking?

It is difficult to overstate just how galling, and enraging, Mrs Clinton and her husband Bill have found the past two months. They both passionately believe that she has a better chance of beating Mr McCain in November, and that Mr Obama would be a more vulnerable nominee.

Since his 12-state winning streak in February — a run that effectively put the nomination beyond her reach — she has won Ohio, Texas, Pennsylvania, Indiana, and in the past week, West Virginia by a massive 41 points, and Kentucky by 35 — two states her husband won twice as President.

And yet, after each win, and the hardening of opposition of white, blue-collar “Reagan Democrats” against Mr Obama, super-delegates have given a collective shrug. Since West Virginia, twenty-two have backed Mr Obama; she has picked up just four. It is almost too much for the Clintons to bare.

“I’d get out if I believed [Obama] had a better chance to win than I do,” Mrs Clinton reportedly told fundraisers and advisers during a cocktail party at her Washington home last week. She refuses to accept the racial divide arguments, and says that the party will unite.

Mrs Clinton has several reasons for staying in. First, the Clintons do not give up. They survived eight years in the White House, including impeachment. Mr Clinton, written off during his own primary campaign in 1992, declared then that he would keep fighting until “the last dog dies”. In a rally in Lexington on Monday he was almost bent double in exasperation as he explained why his wife would be a better president. “They’ve declared her dead more times than a cat’s got lives,” he hollered.

By pressing on through the last three contests — and with a big win in Puerto Rico on June 1 — Mrs Clinton aims to gain further leverage in her argument to get at least half the disputed Florida and Michigan delegates seated at the convention — a move that will probably put her ahead of Mr Obama in the popular vote total when the contest ends on June 3.

That, she hopes, might persuade enough super-delegates to give her the nomination — a long shot, as she needs the vast majority of the 180 who remain uncommitted.

Mrs Clinton also knows how volatile and unpredictable politics can be. There is always the chance, she believes, that a scandal or major blunder by Mr Obama could lead the party to look for an alternative — her. This is what some aides describe as the “act of God” strategy.

In recent days Mrs Clinton has begun insisting that sexism, rather than racism, has been the corrosive influence in the race, and that she has been the victim of a misogynist press. The way she has been treated has been “deeply offensive to millions of women”, she said. She is damned if she is going to be forced from the race when so many women — millions of them — find her an inspiration. The last message that she wants to send them is that she is a quitter.

Of course, Mr Obama might well lose against John McCain. By staying in, racking up votes, and further proving her electability, Democrats would not have far to look for a candidate in 2012 — or even 2016. The Clintons are professionals — and have always been willing to plan long-term.

Times Recommends

• Should Knox’s trial even have reached the courtroom?
• 'Was it real?' The US bailout nightmare
• Iranian opposition plays the long game