the major personal issue remaining is the one of reputation/fame, and accomplishments.
As it is, the Supreme Court has changed course since
Bush v Gore and is presently starting to destroy the pre-2000 'accomplishments' of Rehnquist in driving a particular Right/Conservative (mis)interpretation of the Constitution.
Bans on gay sex
upheld: Bowers v Hardwick, 1986
overturned: Lawrence v Texas, 2003
Capital punishment of the mentally retarded
upheld: Penry v. Lynaugh, 1989
overturned: Atkins v. Virginia, 2002
Capital punishment of under-18s
upheld: Stanford v. Kentucky, 1989
overturned: Roper v. Simmons, 2005
Lawrence more or less blew out the whole argument for making gay people second class citizens, and with that the whole issue of gender-based rights (read: achievement of womens' equality) is revived and the Court is now 'liberal' on it, i.e. expected to permit legalization of gay marriage and tolerate no more attempts to make/keep women second class citizens whatsoever. (This includes tampering with Roe v. Wade.) Rehnquist has lost that charge the Nixon people gave him- upholding DOMA is all that can be done now.
Atkins and Roper are less than abolition of capital punishment (the 'death penalty') but signs that the carving down of it, stalled since the 1970s, which will end in its full abolition is approaching inevitability. (Around 2020 or 2030 in my estimation.) Rehnquist and his Court spent a great deal of time and effort reviving capital punishment from near-abolition in the 1970s, engineering the Romer v Georgia verdict to do so iirc. This charge is also nearly lost to Rehnquist.
There's yet another challenge coming down the pike to overturn a major Rehnquist ruling that has kept Republicans in power and kept criminals who have served their sentences from becoming equal citizens. Rehnquist engineered and wrote the horrible verdict (Google it up, have a look at what the dissents tell of how he took a bad case and used it unconscionably) in Richardson v. Ramirez, 1974, which upheld laws disenfranchising these people and those within the penitentiary system of the vote. He knows that if/when he retires the plaintiffs in the lawsuit about this matter in Florida, Johnson v Bush, will appeal it to the Supreme Court and probably get an overturn.
***
The bottom line is that Rehnquist was put on the Court to stymy all the 14th Amendment civil rights verdicts that the likes of William Brennan were getting through, which constitute the 'liberal' vs 'conservative' stances and the true distinction between 'strict' and 'loose' "constructionism". He got a lot bizarre subversions and perversions of 14th Amendment rights into verdicts, most famously/infamously in Bush v Gore, where the writer essentially claimed that properly counting black peoples' votes amounted to violations of white voters' 14th Amendment rights. Literal black-is-whiteism of the crassest sort, particularly because the 14th Amendment was ratified in 1868 precisely in order to secure former slaves the ability to vote in the South. An absurd mockery of any idea of justice or the 14th Amendment. A perfect travesty.
The 14th Amendment is where the game is and has been for 60 years. It starts with Brown v Board and goes from there- all the progressive court verdicts, even Roe v Wade, are built on enforcement of its rights guarantees. The conservative game has been to try to vaporize them- see
http://www.brennancenter.org/resources/ji/ji5.pdfRight now, if Rehnquist were to leave the Court none of the potential replacements looks to go as far as he can/does in maintaining the remnants of that perverted jurisprudence that Rehnquist calls his legacy and purpose on the Court. I think saving Richardson v Ramirez from overturn would be the most immediate and particular reason in 2005/06, with upholding DOMA and minor others if he can last beyond the year.
Plus, if Rehnquist were to retire now, he might well yet live to see more of his 'accomplishments' overturned- his retirement would lead to reviews of his tenure on the Court and everyone realizing what the game has been, and the score and the trend in it showing him defeated.
That's why he can't retire. If he does, the Cause is Lost. It always was unlikely to prevail, but the supporters thought they could if they never gave up the will, the desire, the initiative. And now it's their 1865.