"I've cried many nights. My daughter deserves better. It's not her fault that her mother and father could not get along and stay married," said a divorcee of three years whose tale of how she has tried, and failed, to get regular child support payments from her ex-husband is one shared by thousands of women in the county, and millions of women nationwide.

Most women don't try as hard, many not at all. "It's so tiring. One battle after the next. I can see why many people say, 'Hey, I give up,'" said the 32-year-old schoolteacher whose daughter is now 5 years old.

Of the approximately 3.4 million single parents in the United States due child support payments in 1978, only half received them, according to a Census Bureau report issued recently. In Montgomery County, a newly expanded staff of 12 in the Circuit Court's Family Services department is trying to monitor 4,700 problem cases, has enjoyed moderate success in collecting payments but readily admits much remains to be done.

The $80 a week due Emily, who asked that her real name not be used, is an amount she and her ex-husband agreed on. It arrived irregularly and increasingly infrequently.

"He knew I would make sure our daughter was okay, had food, clothes and would not feel dramatically the effects of divorce, and he was right. I learned to be very, very conscious of my money.

"She has a pair of shoes for school and a pair for church. If they wear out too fast, she has one pair two purposes. I want her to have a religious education, and had to ask the Sunday school to curtail the membership rate for me. My daughter would like ballet lessons and learn to ice skate, maybe have a mini-vacation. But we can't afford it. She has just enough to get by."

By last December her ex-husband owed her $4,000 and the court ordered an earnings lien -- money deducted by the employer from salary -- and that payments be made through the court. The first payment was due Dec. 3 but arrived Jan. 28. By that time it should have been $720 but she received $383. Thereafter roughly $80 came every two weeks.

When payments stopped altogether she called his employer to be informed he no longer worked there. She called Family Services, the seven-year-old Circuit Court department responsible for enforcing court decrees on domestic relations, where a clerk checked the record, and told her the department would issue her ex-husband a show cause order to appear before the judge and explain the non-payments. They told her to call back in a month.

A month later Family Services reassured her the case was still being worked on. A couple of weeks later a different clerk answered the phone, checked the record, and said it didn't look like anything was being done on the case, but that a show cause order would be issued.

Emily doesn't want to create a scene with her daughter's father when he picks her up every other weekend, and only mentions the money when there are lapses. She told him she had received nothing. On April 11, he sent $44 through the Family Services department. Another $208 came on May 27. One payment came in June, two payments in July and from August, $160 every two weeks. Since last December's court order alone, his debt is $1,300.

The woman, who now owes her attorney $1,500, cannot afford to have the lawyer come to court again to seek back payments, so she will represent herself. A hearing was set for Sept. 19. But when the court tried to summons her ex-husband, he was no longer at the address. They located him and set a new hearing for Oct. 31. Two days before the hearing, the ex-husband's attorney said he (the attorney) had to be out of town. The hearing is postponed for another month.

"With my ex-husband's track record, I'm not optimistic," she said. "He's the type who won't pay unless he's forced. He knows he can get lost in the shuffle."

"The system breaks down after the first court order and the deadbeats know it," said Jo Fogel, a lawyer who handles domestic relations cases. "Are you going to pay a lawyer $40, $50 or $60 an hour to collect $7 a week? It's not productive for anybody."

Since 1975, the federal government, through its Child Support Enforcement Program, has required states to take steps to identify and locate absent parents, establish and enforce support obligations, and collect and distribute support payments.

The program is aimed mainly at collecting payments for single parents who receive a kind of welfare called Aid to Families with Dependent Children (AFDC). Those parents, as a condition for receiving assistance, were required to sign over their support payment rights to the state, which collected the money. The program's assistance is available to non-AFDC parents who ask for help.

Last year Maryland collected $10.9 million from individuals whose ex-spouses were on public assistance, and another $9.9 million that it redistributed directly to non-AFDC families.

But an audit by the Department of Health, Education and Welfare of Maryland's efforts were over a year starting in the fall of 1977 found that services were not always available to everyone and that 65 percent of support obligation cases reviewed were not properly enforced.

The Montgomery County Circuit Court's Family Services Department receives child support payments from 4,700 parents who are either ordered by the judge to pay through the court or who receive public assistance. Delegate Ida G. Ruben (D), is sponsoring a local bill that would require all payments to be made through the court so that enforcement would become automatic when payments stopped.

"Now, the judge may order payments to be made through the court, but few are ordered. We should reverse the law and mandate the court to receive payments unless the judge feels it is necessary," she said.

Democratic Delegate David L. Scull, who estimates the collection rate locally is 20 percent of what is owed, is working on a bill that would have child support payments withheld with taxes and paid to the comptroller.

Barbara Bergmann, professor of economics at the University of Maryland who is writing a book on child support, believes Scull's bill would be more effective in getting payments than a court order. "What's a court order? You don't know what it is until you violate it."

"It all comes down to society's reaction to authority.A court order is in effect a law. Some people abide by it and others don't" said Fogel.

Jail sentences are rarely given for negligent parents. Judges more frequently extract a promise of payment by a certain date or order an earnings lien.

County Clerk Howard Smith, who heads the court's Family Services department, said that with the additional staff and a data processing program that should be completely installed by January, the record of payments should improve. Negligence will come to the attention of the staff sooner, and automatically. The state attorney's office and the social services department will have their own computer terminals and access to information they now get from Family Services by telephone.

During the past year the department collected more than $2 million. Smith said that in less than a year he hopes the department will double its collection. He does not have figures on the total amount owed.