THIS HAS BEEN A blues year for Caroline Thompson. And the blues go on.

Her daughter 13, has run away 15 times within the past year. This time she's been gone for three weeks. Thompson has been searching streets and alleys herself because "the police aren't doing anything." Her hands tremble on the wheel on the borrowed car as she approaches the building on Delaware Avenue SW where she was told Betty might be. In the hallways, the smell of urine stings her nostrils; trash overflows from incinerators, blocking her passage. Her daughter's friend has accompanied Thompson and knocks on the door and asks for Betty. In a minute, the girl walks uncertainly into the stinking hallway. She looks terrible.

The mother's hazel eyes are wet. She is 30 and a single parent of two girls. The names of Caroline and Betty Thompson are fictitious, but their story is not. Caroline feels the system in this city has completely broken down for people like her and Betty, her older daughter. She's found no institution that has been able to help her save her child from the swirling vortex of drugs, rape, academic chaos and illness that is engulfing her. Her daughter is one of this city's hundreds, maybe thousands of "lost" children.

She asks the girl to come home.

"I have something to do. I'll be home tomorrow," Betty says gruffly, wheezing from a bad cold. The girl is as high as a satellite.

When her daughter hurries back inside the housing project apartment, Thompson knew she couldn't "leave my child" there. Walking resolutely down the stairs, she asks a man on the street for directions to the nearest police station. Youth Division officers accompany her back to get Betty because Thompson convinces them the apartment is occupied totally by minors. The teen-ager is such a whirlwind of fury that they take her away in handcuffs.

If adolescence today is a roller coaster ride for all parents of teen-agers, it is a nightmare in full wakefulness for those in our city who can't afford to buy the held they need, and must therefore depend on public services and institutions.

Caroline Thompson has tried Juvenile Court, the schools, drug treatment centers at St. Elizabeths Hospital in a vain attempt to save her daughter. It is an alarming situation because her daughter's rebellion is representative of a growing number of less affluent adolescents between the ages of 9 and 15 who are children of post-World War II single parents here. Many of their problems are tied into the larger socioeconomic pressure, but they also are exacerabated when the video world of electronic plenty collides with their own of joblessness, ready drugs and troubled schools.When families succeed in putting a roof over kids' heads, they're sometimes too exhausted and resentful to provide a loving atmosphere. Where those of us in another generation took out our frustrations on the system, these children of the 1960s take it out on their parents, condemning their parents' powerlessness and poverty. Too often a sense of familyhood is missing.

Caroline Thompson is a product of a troubled home and vowed after bearing her daughter out of wedlock at age 16 that Betty's life would be different than her own childhood. She oversaw homework, bought her daughter good clothes, and fought against street influences. But she was also away from home a lot. "Maybe I pressured her too much," she says.

Betty's troubles began in the seventh grade, about two years ago, when she started playing hooky. Thompson said she wasn't informed about her daughter's truancy until well into the year when she called while she was at her secretarial job in the federal government. By then Betty was not only skipping school, but smoking pot and engaging heavily in sex. Caroline Thompson took a part-time job in order to move from Brightwood in Northwest D.C. to Riggs Park in far Northeast, to a new school where Betty promised to start a "fresh new life." Shortly after that, Betty's estranged father was found murdered in Rock Creek Park in a drug-related crime.

"She didn't want to go to school because the kids teased her and she couldn't keep up," Thompson recalls. "Her father's death had a big effect on her. She really loved him and deep down inside I think she wished he was a better man and a better father to her. I think her hopes vanished. He loved her in his own way but he was just a junkie. What can you do when you're a junkie?" What Thompson was never able to explain to her daughter was that her father also was a victim.

Thompson now admits she may have lost touch with her daughter at some critical juncture. The pattern of running away started when Thompson once tried to discipline Betty for truancy and promiscuousness. By now she'd discovered Betty constantly cursed her teachers. Boys had begun calling her to tell her the girl was "a whore". Thompson lashed out and hit Betty for her disrespectful "mouthing off." The girl took off, and she's been running since.

On the occasions she was able to get her home or with other relatives, Thompson enlisted friends to talk to the girl. "I tried to interest her in herself . . . took her to a modeling course, she still didn't change."

"I haven't slept in God's knows when," Thompson said the other day, fingering a bandana."My hard has come out. Sometimes I feel real dizzy when I walk. It's tension. The hardest thing is not knowing whether the child is dead or alive."

Betty's response when her mother seeks and finds her time after time: "I just want to be free."

Passing her hand over a freckled forehead, Thompson says: "What's free when you're 13? I don't think she cares if she is dead or alive. She even told me once she wished she was dead. I've never let her live in a world of fantasy. She knows how this world is out here. She's been raped two times and she didn't even know it. She's rebelling against school because she feels she's dumb. She wants help but she's so hostile."

The Youth Division of the Police Department said it had 1,845 reports of juveniles missing in the fiscal year that ended September 1980. "With over 1,800 cases a year we don't send dogs and helicopters out for every person missing," said Sgt. Robert Seguin, who added that most of them eventually return home.

Last month, after Thompson found Betty on Delaware Avenue, the police took her to the Receiving Home Overnight and the next morning they went to court. But Thompson's petition to have her daughter declared beyond her control and committed to a foster home or Cedar Knoll, the District's home for delinquents, was dismissed. The two left the court and returned home. The next day Betty ran away again.

She stayed away three or four days until a relative found her and brought her home. Since then, she's run away several times.

She's gone right now.

"I'm tired and depressed," Thompson says. "But I'm trying to be strong so I can think. I don't have no choice really.I've got another lead. I'll call the police and see if they can pick her up and we'll go to court and start all over again."

There are thousands of single household heads here who have escaped Thompson's fate, but even they lack society's full respect and support. Unless we try to negotiate other definitions of family and help troubled adolescents and parents, there will be more Bettys. Meanwhile, the blues goes on for Caroline Thompson.