RINDGE, N.H. — Amber Jackson remembers the moment she learned that both her majors — dance and math — had been cut from the program at Franklin Pierce University. She immediately called her mother, whose reaction was: “They can do that?”

They could.

After years of financial crisis, Franklin Pierce, like dozens of other small colleges nationwide, is struggling to survive. It faces huge debt, a junk bond credit rating and an uncertain future. It has even resorted to creative image-buffing, like hanging a banner on a derelict building here saying, “Future Home of the Franklin Pierce Science Center,” though there is no money for a science center yet.

This year, there is a glimmer of hope. Applications were up 79 percent, an unlikely side effect of the university’s decision to revive a political polling operation in a hot election year. But as Andrew H. Card Jr., who took over as university president about 15 months ago, said, “One year does not a trend make.”

Still, he said, “I breathed a sigh of relief.”

In the last few years, small liberal arts colleges have been under financial siege, forced to re-examine their missions and justify their existence. Even several established and respected ones — Bard College, Yeshiva University, Mills College and Morehouse College, among others — have received negative financial ratings.

Not that long ago, colleges across the country enjoyed a seemingly endless supply of candidates and were pouring money into expansion plans. Some added costly luxury amenities like rock-climbing walls to seem more attractive. Some increased tuition on the theory that high tuition connotes prestige, but then cut their cash flow by giving out generous scholarships and grants to lure students despite their price. (At Franklin Pierce not a single student pays the sticker price.)

Now, as times change, the colleges are fighting over a dwindling pool of applicants. In parts of the country, the number of high school graduates is dropping. At the same time, students and parents have started to question the choice of expensive private schools that leave them with high debt and no clear job prospects, taking a second look at public universities. And the reduction in demand is making it harder to pay for some of the overbuilding.

Smaller colleges are especially hard-hit. Many of the endangered ones are in rural areas and have traditionally drawn from regional markets, but have lost market share as students become more willing to travel beyond their home territory. Often they have not been able to keep up with the demand for expensive science and technology courses.

Some are women’s colleges, historically black colleges or religiously affiliated — appealing to a smaller audience.

Franklin Pierce has about 1,400 undergraduates on its tiny rural campus in Rindge, N.H. Credit Gretchen Ertl for The New York TimesPhoto by: Gretchen Ertl for The New York Times

They also tend to be less selective, with anemic or highly restricted endowments that make them overly dependent on tuition. Their alumni do not provide as much support as those of elite small colleges like Amherst, Swarthmore or Grinnell, which have powerhouse endowments.

“Everybody’s competing for the best and the brightest,” said Karen Kedem, vice president and senior credit officer for higher education at Moody’s Investors Service, whose ratings can influence fund-raising and accreditation. “It makes it harder when you go down the food chain.”

Among institutions that have closed in the last two years: Sojourner-Douglass College, in Baltimore, a predominantly black college that is waging a court fight to reopen; Marian Court College, a 50-year-old Catholic commuter college 15 miles from Boston that had been squeezed by the crowded New England market; Lexington College, a Chicago women’s college specializing in hotel management; and Mid-Continent University, a Baptist institution in Western Kentucky, now in bankruptcy.

Moody’s estimated last fall that the number of four-year, nonprofit public and private colleges going out of business could triple, to 15 from five a year, over the next few years. The merger rate would more than double from the current two or three.

Yet despite their problems, many colleges prove to be surprisingly resilient. Probably the most famous recent example is Sweet Briar College, a century-old women’s institution in Sweet Briar, Va., which was saved from extinction last year by legal action and the last-minute efforts of alumnae.

Antioch College, a crucible of 1960s radical protest in Yellow Springs, Ohio, closed in 2008, only to pull off the rare feat of reviving in 2011.

But for every college that has pulled off a rescue, there is one in trouble. Moody’s has criticized Bard, 100 miles north of Manhattan, for having little cash and relying on a few rich benefactors. “We operate under a different model,” Leon Botstein, Bard’s president, said in an email. “We’ve never operated under a deficit, and have raised over a billion dollars over the last 40 years.”

Yeshiva University was forced to transfer financial responsibility for its medical school to its teaching hospital system last fall. It has been hampered by competition from lower-priced public colleges and by its heavy dependence on a niche undergraduate market of Orthodox Jews, according to Moody’s.

A Yeshiva spokesman, Paul Oestreicher, said that after making some adjustments, the university was on “a pathway to responsibly achieve financial stability while assuring operational and educational excellence.”

James Wolken, Franklin Pierce’s marketing director, with mock-ups for a fall marketing campaign. Credit Gretchen Ertl for The New York TimesPhoto by: Gretchen Ertl for The New York Times

Franklin Pierce has about 1,400 undergraduates on its tiny rural campus, tucked here between the choppy waters of Pearly Pond and Mount Monadnock, a popular hiking spot memorialized by Ralph Waldo Emerson. With an endowment of $5.2 million and debt of $39 million, it depends on student fees to pay more than 95 percent of its operating costs; yet to keep students, it must heavily discount its $46,000-a-year tuition, room and board.

At its nadir in the fall of 2014, it hired a new marketing director, James Wolken, who had worked at the Massachusetts Institute of Technology and the Rhode Island School of Design. He sat in his office recently surrounded by mock-ups for a fall marketing campaign — “Be Frank. Be who you want to be at Franklin Pierce” — and recalled how he had pushed to revive the college’s political polling operation, abandoned during the 2008 recession.

Mr. Wolken argued that the poll would build on the college’s Marlin Fitzwater Center for Communications, and give the Franklin Pierce name new visibility. The trustees argued that presidential elections come around only once every four years, and that the university needed a more permanent boost.

But Mr. Card, a chief of staff in the last Bush administration and new to his job here, liked the idea.

Last spring, the university formed a partnership with The Boston Herald and a private pollster. The unexpected intensity of the election season attracted attention to the operation for 11 months before the New Hampshire primary. Mr. Card leveraged his White House credentials to offer political commentary. And in August, worldwide news media picked up a Franklin Pierce University/Boston Herald poll showing Senator Bernie Sanders of Vermont leading Hillary Clinton in New Hampshire.

The name recognition was phenomenal. “CNN, Fox, regional TV, he always got our name plug there,” Mr. Wolken said of Mr. Card.

In September, Standard & Poor’s raised Franklin Pierce’s rating from a gentleman’s CCC to CCC+, Mr. Card recalled.

This year, undergraduate applications soared to more than 6,400, from 3,600. More than 500 students have put down deposits, up from 370 at the same time last year. Officials say their goal is a class of 540.

Like the college, Amber Jackson has survived. She will graduate this spring, a major in math because declared majors were allowed to continue, and a minor in dance.

“That was a really hard thing that I had to go through,” Ms. Jackson said. “I had to fix not just one but two majors.” Still, she said, “Over all, I had a really good experience.”