The D.C. Public Charter School Board on Monday rejected a request from BASIS DC to expand, citing concerns about the high number of students who have withdrawn from the charter school since fall.

BASIS, an Arizona-based chain of charter schools known for its rigorous academic demands, won approval to open doors in the District in 2012 despite questions about whether its model would work for struggling D.C. students. At BASIS schools, middle-school classes are accelerated and students must take and pass a heavy load of Advanced Placement courses to graduate from high school.

The school received city funding for 443 students, the number it had enrolled on Oct. 5. Since then, 43 students — almost 10 percent — have left the school. Seven of those who left were students with disabilities.

Board members said the high rate of attrition raises concerns about BASIS’s ability to serve all children, but the departures from BASIS also touch on broader debates about how D.C. education is funded and whether traditional neighborhood schools end up serving as a safety net for students who leave or are expelled from charters midyear.

The city’s funding rules allowed BASIS to keep hundreds of thousands of dollars in per-pupil allotments for the students it lost after Oct. 5, while the schools that received those students got no additional money.

Paul Morrissey, head of school for BASIS, said attrition is often high in the first year of operation of a BASIS school, but enrollment stabilizes as students and families learn what the program demands. Nearly 25 percent of students withdrew from a BASIS school in Peoria, Ariz., during its first year of operations, he said.

“When a BASIS school comes into a new market, there are students who understand and know what the workload is and what it takes to be successful at BASIS, and there are students who are not prepared to do that kind of work,” Morrissey said.

The BASIS charter agreement allows the school enrollment cap to automatically rise by 43 students to 511 next year, accommodating the addition of ninth grade. School officials asked the charter board for permission to enroll an additional 35 students, saying they need to bring in more money to make loan payments and to pay rent on their Penn Quarter building.

The BASIS lease was structured so that this year’s rent, about $1.1 million, will nearly double next year to $2 million.

Charter board members largely dismissed the argument that the school needs more money, instead asking for an educational justification for the requested enrollment increase. BASIS officials said they had to hire more staff and implement more programs than they had anticipated in order to support struggling students.

Morrissey, the head of school, argued that the board should approve the enrollment increase on the strength of the nonprofit BASIS charter network’s national and international reputation. But board members were more interested in the school’s performance in the District.

“I don’t think we know enough about the success of your program, at least here in D.C., to approve your request for growth at this point,” Vice Chairman Darren Woodruff said.

The board also turned down a request from Creative Minds to increase its enrollment by 12 students. Like BASIS, Creative Minds is a first-year school.

The charter board granted nine more-established schools permission to expand, increasing their enrollment next year by a combined total of more than 1,300 students.

The nine schools that won permission to expand are: Carlos Rosario, DC Prep, KIPP DC, Next Step, E.L. Haynes, Education Strengthens Families, Excel, Paul and Washington Yu Ying.