For the past several months, three-year-old George Carter has spent every weekday morning at a District-run Therapeutic Nursery School - a program for children whose emotional problems make it difficult for them to function in regular nursery schools.

But Friday, George, who is hyperactive, and his five classmates who attend the afternoon session will probably have to stay home or go to day care centers. Their teacher, Mrs. Lyang Thorpe, is among 45 employees of the Area C Community Mental Health Center who have received termination notices from the department of human resources. The 45 positions were funded by an eight-year National institue of Mental Health grant that expires March 31.

"We're trying to shift some money around to keep Ms. Thorpe on until June," said Francis Queen, director of youth services for the center. "But we still don't know whether we're going to be able to do it."

According to Ollie Brown, administrator of the center, the department has picked up 11 of the 45 positions funded by the expiring grant. The Area C Community Mental Health Center, which serves Southwest, currently has a staff of 175. There are about 275,000 people living in the area.

The position cuts mean that services to area residents will be severely curtailed. The Therapeutic Nursery School at 337 North Carolina Avenue SE will close and another, located in Payne Elementary School at 15th and C Streets NE, will lose the counselor who works with parents. A therapeutic school for 25 older children will be left with only one teacher.

The evening mental health clinic for adult outpatients will also be discontinued. An all-day treatment center for alcoholics will be left with one staff member to handle 20 to 25 patients and may have to discontinued. Other programs will lose the services of physicians, psychiatrists, social workers and occupational therapists.

Brown said that the eight-year "growth" grant was made with the understanding that the District would evenutally fund the programs, but that there is no money available to fund all of the positions now covered by the expiring grant.

Several employees of Area C have criticized both DHR and Mayor Walter Washington for failing to find funds to continue these programs.

In a letter sent last week, 19 employees - including some who are faced with job loss and some who are not - told Washington that "it is difficult to understand why there has been no recognition of or response" to appeals and suggestions for ways to keep on workers whose salaries were paid by the expiring grant. The appeals came from "many different agencies, members of the City Council, special interest groups and concerned citizens," the letter said.

City Council member David Clarke has also critized the mayor and his staff for failing to request funds from the Council for the mental health programs. "There was no flag to the problem," Clarke said. The positions that would be unfunded when the grants expired were not noted in the mayor's fiscal 1977 budget, according to Clarke.

Some parents of children in affected programs are also appealing to the mayor.

"I'm writing a petition and taking it door to door and on the street for people to sign and I'm going to send it to Mayor Washington," said Grace Carter of 1226 Morse St. NE, the mother of three-year-old George, who attends the Therapeutic Nursery School.

"It's worrying me to death that the school will close. Before I found that school George was climbing the walls and I was climbing the walls.He used to be very nervous and have seizures. Now he pays attention - he's more settled.

"A child doesn't grow up in a vacuum," said Eular Robinson, a social worker who works with children at the school and counsels their parents. "We have weekly therapy sessions in which all the parents get together to talk out their problems."