WASHINGTON, Nov. 18— The house is peaceful as the college student, a mother's helper, feeds a premature baby her bottle of formula. The only hint of anything unusual is a small electronic monitor that rhythmically flashes two green lights, indicating that the baby's heart rate and breathing rate are normal.

Suddenly the rhythm of flashes is disrupted. A red light turns on, and a steady beep, beep, beep warns that the heart rate has fallen to dangerously low levels. The tiny baby turns pale, closes her eyes, and hangs limp as a rag doll in the frightened student's arms.

From across the room, the baby's mother swoops to the rescue, lifts the infant, and turns her upside down. A spray of milky liquid belches from the baby's mouth. Color returns to her cheeks, and a childish wail fills the air. The unnerving beeping stops. As abruptly as it started, another brush with death has been averted.

Such back-from-the-brink dramas are now becoming part of everyday reality as tens of thousands of parents assume responsibility for monitoring, and often resuscitating, infants who are at increased risk of dying because of prematurity or other ailments. Pressure of Responsibility

Medical advances and new patterns of care have combined to place life-and-death decisions that were once reserved for hospitals and doctors in the hands of the parents. The pressure can be enormous as parents face the reality that their child's life may depend on how quickly they respond to danger and how competently they apply revival measures.

For the parents, the experience can be nerve-wracking as well as reassuring. Several studies show that parents are often acutely anxious for the first few weeks. They are frequently exasperated by equipment malfunctions, fatigued and irritable at responding to the alarms, some of which are false, and overwhelmed by fear and tension if they are required repeatedly to resuscitate a limp baby. But many parents eventually become so dependent on the monitors for reassurance that it is difficult to wean them off the machines when their infant is pronounced well.

The monitors are the most visible part of a home care revolution that has seen a wide range of other medical technologies adapted to home use, including ventilators to help a sick child breathe, and intravenous infusion pumps to provide nourishment. 'An Explosive Growth'

''There has been an explosive growth in home monitoring,'' said. Gary Harding, a senior consultant for ECRI, a nonprofit organization in suburban Philadelphia that analyzes health care technology for hospitals.

George Jackson, the president of Aequitron Medical Inc., a small Minneapolis-based company that is the major producer of home monitors to detect apnea, or cessation of breathing, and abnormal heart rates, said: ''Ten years ago there was relatively little monitoring; parents would just lose a child and feel guilty. Five years ago there were probably 15,000 to 20,000 children on home monitors for apnea. Now there are reports that, at any given time, 35,000 to 40,000 children are being monitored.''

The Food and Drug Adminstration estimated last year that 40,000 to 45,000 apnea monitors were already in use and that each year 12,000 to 15,000 monitors, both new and used, were sold.

Indeed, home monitoring has spread so rapidly that some experts fear it has gone too far, with anxious parents hovering over monitors in cases where there is little real danger to the child and little chance the monitor will serve any purpose.

''The whole home monitoring business has gotten way out of hand,'' said Dr. John Scanlon, director of neonatology at the Columbia Hospital for Women in Washington. ''I try to discourage a lot of it.'' Outgrowth of Medical Advances

The upsurge in home monitoring is a natural outgrowth of medical advances that have allowed doctors to save extremely premature babies, often weighing two pounds or less, that would have died if they had been born just 10 years ago. These infants are cared for in hospital intensive care nurseries until they are healthy enough to go home.

Even then, however, some premature infants remain prone to occasional unpredictable episodes in which their breathing rates plummet for 20 seconds or more, taking their heart rates to low levels as well. The danger of such attacks can persist for months, or even a few years. Only with a monitor can the parent hope to detect such episodes promptly enough to take action within the few minutes before the child suffers irreversible harm or death.

Home monitoring has also been propelled by cost-containment drives that seek to push patients, even premature infants, out of the hospital as soon as possible; by aggressive marketing on the part of manufacturers, and by doctors' fears of malpractice suits if they fail to prescribe a monitor where one could prove useful or parents request one.

Many parents virtually demand monitors in the belief, supported by little evidence, that the monitors can help prevent sudden infant death syndrome, the mysterious illness that kills about 7,000 apparently healthy babies in the United States each year. However, most experts believe there is little connection between the infantile apnea attacks detected by the monitors and deaths caused by by the syndrome. Several reports indicate that no more than 7 percent of the victims of the syndrome were noted to have prolonged apneic episodes before dying. Experts Set Guidelines

A panel of experts assembled by the National Institutes of Health last year recommended home monitoring for only a small proportion of infants, even among those born prematurely or having brief episodes of apnea. It recommended monitoring only for those who had suffered an apparent life-threatening apnea attack requiring vigorous stimulation or mouth-to-mouth resuscitation; premature infants who continued to have severe apneas when otherwise ready for hospital discharge, and infants with certain specific diseases.

The panel estimated that 7,200 to 18,000 infants might require monitoring each year, and that it might prevent death due to apnea in some.

The panel also concluded that several other groups of infants faced an increased risk of death but that the value of monitoring in these cases was inconclusive, to be decided by the family after discussion with a doctor. Such infants included those born to parents who had lost a previous child to sudden infant death syndrome, those who have experienced an apparent life-threatening episode that did not require vigorous resuscitation, those who require a surgical hole in the windpipe to breathe and infants born to certain drug-abusing mothers,

Diagram of electronic monitor