LAST MARCH Atlanta's 106-year-old Bishop College lost its accreditation. The historically black private college is at least $11 million in debt and has filed for reorganization under Chapter 11 of the bankruptcy code. When school opens this fall, enrollment is expected to reach only 450 students, less than half last year's.

Some 325 miles to the northeast in Greensboro, N.C. at another predominantly black college, the situation is very different. At North Carolina Agricultural & Technical University, alma mater to Jesse Jackson and astronaut Ronald McNair (killed in the Challenger explosion), chancellor Edward B. Fort is moving the university increasingly into the field of scientific research, which has paid off handsomely. Five years ago the National Aeronautics and Space Administration awarded the university a $10,000 grant to develop pay loads for the space shuttle. And today, in addition to its state subsidy, N.C. A&T receives about $9 million annually in federal grants for scientific research.

"I think this is a turning point in the mission of black colleges," said Fort. Black colleges that fail to move ahead with the times "will go down the tubes."

For the last century or so, more than 100 colleges pursued a mission of educating students who, until recently, were not welcome at white institutions. They turned out black teachers, preachers, doctors and lawyers to serve the black population in a segregated society. And they enrolled disadvantaged and rural youngsters who otherwise would have been overlooked by the educational system.

Today, many of them serve some of the country's most disadvantaged students, have slim endowments, and lack financial resources to develop programs to compete with other schools, now desegregated. Even the strongest black colleges are facing stiff competition from Ivy League and other well-known institutions for the best black students and faculty.

Frank Matthews, publisher of the magazine Black Issues in Education and assistant senior vice president at George Mason University, predicts that as many as half the nation's black colleges may close their doors in the next few decades.

Others guess that at least one-third of the historically black colleges -- which number slightly over 100, depending on whose count is used -- have problems that threaten their survival. And the foremost problem, particularly at the private colleges, is money.

For one thing, black students tend to be poor. In 1983-84, more than 80 percent of students at private black colleges qualified for financial aid. And the median family income for those black students was $10,733, or about one-third the median for all families with children in college, according to a recent report by the United Negro College Fund and the National Institute of Independent Colleges and Universities.

And because their students are poor, private black colleges charged an average tuition of $3,233 in '85-'86, compared with $5,428 average tuition at private colleges nationally.

"Our resources are stretched because we can't charge the tuition we need to charge," said Norman Francis, president of Xavier College in New Orleans, where tuition is $4,300.

Many black colleges also find it difficult to build up their coffers with gifts from wealthy alumni. "Their graduates don't go on to major corporate jobs and become millionaires," noted Reginald Wilson, director of the office of minority concerns at the American Council on Education.

As a result, the average endowment per student at a United Negro College Fund member school is about half that for a four-year private college.

While they may be more financially secure, the public black colleges face another threat. Acting to desegregate their campuses, some states, among them Kentucky and West Virginia, have merged black colleges with their predominantly white counterparts or closed the black campuses altogether.

At least five historically black state colleges that have been merged now enroll a majority of white students, said Wilson. "A like phenomenon is not happening in white schools, so there's a loss of black students overall," he added.

Wilson said the number of black students in institutions of higher education dropped by 37,000, to 1.07 million, from 1980 to 1984.

At the same time, the best and the brightest black students are being aggressively recruited by Ivy League and other prestigious schools. Given a choice, "the best black students are going to enroll at white colleges, which are preceived as being better," Matthews said.

Vanessa Baird, for instance, chose Dartmouth College over Spelman College, a respected black women's school in Atlanta. The 20-year-old New Yorker had attended a parochial high school and "didn't know if I wanted to drastically change my environment by going to a predominantly black institution."

If there is a shakeout of black colleges, however, Spelman is a likely survivor. In the late 1970s, then-president Donald M. Stewart decided it was time to get aggressive in both recruiting and fundraising. As a result, Spelman saw its applicant pool double and its endowment jump from $9 million to $49 million in about three years.

"I think any school could do what we did," said Stewart, now president of the College Board in Princeton, N.J. "But it does take money and all too many historically black colleges do not have money."

Even some of the most venerable black institutions are not immune from problems. Fisk University in Nashville, founded in 1865 and alma mater of W.E.B. DuBois, Paul Robeson and many other prominent blacks, almost lost its accreditation in 1983, as it struggled with more than $4 million in debts and declining enrollments.

Because of its status, Fisk got a lot of publicity and a lot of help from the federal government, the local community, alumni, churches, foundations and corporations.

Henry Ponder, who has been president at Fisk for three years, said last year's enrollments were up for the first time since Fisk's troubles began. "I think we've turned the corner," he said.

NEW PROGRAMS and creative approaches to student recruitment seem to offer the best hope for black colleges caught in difficult changing times. "I lose patience with colleagues who suggest they don't have a chance," said A&T's Fort.

For instance, this year six black colleges will receive $5 million grants from the National Science Foundation for the purpose of setting up research centers. The Foundation is reviewing applications now and will announce the grants by the end of the year.

Xavier College has developed a special niche for itself with a program to bring black high school youngsters interested in the sciences to campus for a summer program. The program, SOAR (Stress on Analytical Reasoning), has helped identify and recruit bright students for Xavier itself.

Xavier recently got a grant to start a similar program for high school students interested in the arts, humanities and social sciences. "We want them to be PhDs," said Xavier president Francis, citing the dearth of black faculty. At Xavier, for instance, only about half the faculty is black.

Howard University, which exists in something of a state of grace because of a hefty federal appropriation, which this year topped $170 million, also faces the problem of developing and keeping black faculty. Spokesman Henry Duvall said one of Howard's biggest challenges is to "ward off the raiding of our faculty by white schools."

Meanwhile, some question whether weak or marginal institutions -- black or white -- are worth saving. To this, Matthews argues that some of the weakest black colleges are those that take a chance on unproven students who would not be accepted elsewhere in the educational system.

"White colleges measure success in terms of input, such as SAT scores, and black colleges in terms of output," he said. "Black colleges brag about how many kids they send to medical school, law school, how many PhDs they turn out, how much progress students make in four years. That's why it would be a tragedy for black colleges to fold."

Debbie Goldberg writes frequently about education.