News that the New Republic, the 101-year-old political and cultural magazine, is for sale is a press business story, but the more newsworthy aspect of it is the political story.

The press business story is that small, standalone publications have a hard go of it, even when backed by deep-pocketed proprietors. As the magazine’s owner, Chris Hughes, a Facebook co-founder who says he has sunk more than $20 million into the magazine over four years, put it, “I underestimated the difficulty of transitioning an old and traditional institution into a digital media company.”

Mr. Hughes is the latest in a series of intelligent and well intentioned owners who have had a go at putting the publication on sustainable footing. I know and have high regard for quite a few of his predecessors.

But the bigger issue isn’t a collapse of circulation or advertising revenue or the publishing industry’s digital transformation. Underlying the New Republic’s difficulties is a broader and far more troubling collapse of the ideology — call it Cold War liberalism, or the center-right wing of the Democratic Party — that once animated the magazine.

What did the New Republic stand for? Under the long editorship of Martin Peretz, if the magazine stood for anything, it was the idea that Israel had reliable allies — and Islamic extremism had reliable enemies — among the American intellectual center-left elites. That certainty is now gone, as evidenced by, among other things, the paltry opposition in the Democratic Party to President Obama’s Iran nuclear deal. Senator Schumer and Rep. Nita Lowey of New York voted to block the deal, but theirs was a lonely stance.

Under Mr. Peretz, the New Republic editorialized in favor of the North American Free Trade Agreement, entertained doubts about the justice and efficacy of race-based affirmative action, supported American military intervention in Bosnia, published a devastating takedown of Hillary Clinton’s health care plan, and otherwise displayed an admirable independent-mindedness. It was a counterpoint to the blame-America-and-capitalism-first attitude of other left-of-center publications such as the Nation or Mother Jones. It wasn’t clear that Mr. Hughes was interested in pursuing that political agenda, or that, even if he was, there was an audience remaining for it.

By this analysis, the New Republic’s troubles are symptomatic. The magazine’s recent influence probably peaked under the center-right New Democrat presidency of Bill Clinton. The Clinton now running for president, Hillary, supported the Iran deal and opposes President Obama’s Trans Pacific Partnership free-trade deal. She’s further to the left than Bill was — and even she is the more centrist candidate in the Democratic primary compared to the socialist senator from Vermont, Bernie Sanders.

Mrs. Clinton is so far left that Michael Bloomberg is reportedly polling on the question of whether there would be room for him to run an independent campaign in a general election presidential race that includes her and Donald Trump.

The Democratic Leadership Council, the center-left vehicle that Mr. Clinton rode to power, closed up shop during President Obama’s first term. It was eulogized in the New Republic in an article that included the line, “it’s laughable to read the reactions from conservatives like the Wall Street Journal’s John Fund, arguing that the DLC’s demise proves there’s no room in Obama’s Democratic Party for ‘centrists.’”

Not that centrists have a lot of room in the Republican Party, either. But for those who value ideological diversity and independent thinking, or free markets, freedom, and a robust, internationalist foreign policy, the New Republic’s troubles are a matter not for laughter but for sadness. Magazines and their owners come and go, but for the Democratic Party to slide fully back into a kind of George McGovern-Jesse Jackson morass would be too bad not just for the New Republic but for our republic.

Mr. Stoll is editor of FutureOfCapitalism.com.