The phrase — is dead but won’t lie down is used of someone who won’t admit defeat.

For example, in The Guardian (Manchester, Greater Manchester, England) of Wednesday 7^th August 1974:

– the banner headline said:

Nixon ¹ is dead—but he won’t lie down

– and Helen Pick, writing from Washington, D.C., explained:

President Nixon is still trying to resist the growing crescendo of powerful voices calling for his resignation. He is displaying a masochistic determination to stay in office until the bitter end.

¹ The Republican statesman Richard Milhous Nixon (1913-1994) was the 37^th President of the USA from 1969 to 1974; he resigned from office, owing to his involvement in the Watergate scandal.

The phrase is of American-English origin. The earliest occurrence that I have found refers to physical weakness; it is from The Clarion Democrat (Clarion, Pennsylvania) of Thursday 2^nd June 1892:

If Republican authority is to be accepted neither Blaine ² or Harrison ³ is fit to be President. Harrison’s friends say that Blaine is a physical wreck, Prince Russell giving it as his opinion that Blaine is so broken down he can scarcely write his own name—in fact, that he is dead, but won’t lie down. Blaine’s friends claim that Harrison is an icicle; that he is so frozen he chills everything and everybody. It is more than possible that when the elections takes place it will be found that a majority of the people of the country accept this Republican testimony, if either of these men are the candidate.

The following paragraph, from the same issue of The Clarion Democrat, also mentioned the subject:

Mr. Blaine sat for a photograph a few days ago, in New York. It is supposed he wants to convince the people he is neither dead nor dying, as Harrison’s friends claim.

² The Republican statesman James Blaine (1830-1893) served as Speaker of the U.S. House of Representatives from 1869 to 1875, and as Secretary of State in 1881 and from 1889 to 1892.
³ The Republican statesman Benjamin Harrison (1833-1901) was the 23^rd President of the USA from 1889 to 1893.

The second-earliest occurrence of the phrase that I have found is from an article on the prospects of the baseball clubs of the American League, published in The St. Louis Star (St. Louis, Missouri) of Tuesday 11^th April 1916:

The Big Three of the American League is composed of Boston, Detroit and Chicago. The Red Sox, the White Sox and the Jungaleers have grabbed off all the available spotlight in the Johnsonian circuit since the passing of the Macks.
The most interesting proposition before the American League on the eve of the big race is whether the Browns, the New York Yanks and the Washington Nationals can make this Big Cinch share some of those calcium rays. Cleveland has Speaker ⁴. Philadelphia is dead, but won’t lie down.

⁴ The same article described Speaker as “one of the High Priests of baseball”.

The phrase then occurs in the account of the sermon that the Rev. C. H. Reckard, pastor of the First Methodist Episcopal Church, gave on Thursday 30^th November 1916 at the union Thanksgiving service in the Greenside Avenue United Presbyterian Church, in Canonsburg, Pennsylvania—account published the following day in The Daily Notes (Canonsburg, Pennsylvania) of Friday 1^st December 1916:

In referring to the election of M. Clyde Kelly in the Thirtieth Congressional district and Guy E. Campbell in the Thirty-second district, the Rev. Mr. Reckard, near the close of his address, said: “The people took things in their own hands and elected Kelly and Campbell. The trouble with Barchfeld, defeated by Campbell, is that he is dead, but he won’t lie down—he can’t understand how it happened.”

The phrase is used punningly in the following paragraph from The Evening Republican (Columbus, Indiana) of Monday 14^th June 1920:

DEAD MAN’S CLUB IS SOLDIER’S SUGGESTION.
(By Associated Press)

Akron, O., June 14.—A dead man’s club, composed exclusively of ex-service men now living but listed officially as killed in action overseas, is the latest kind of fraternal organisation suggested by William Wirt of this city.
Wirt is having a hard time trying to convince the government that he isn’t dead and buried in France. His name now is being chiseled from the memorial bronze tablet recently erected here in a memorial building.
Wirt estimates there are nearly 2,000 ex-service men now living, whom the war department records show were killed and buried overseas. He also declares that court records show about 900 men declared officially dead who are still alive. He suggests they organize a “Dead Man’s Club” and adopt the slogan, “We may be dead but we won’t lie down.”