But while some infertile couples may find the result reassuring, experts noted, many others are likely to struggle with the expense and emotional upheaval of repeated treatments.

The study included nearly 157,000 women in the United Kingdom who together underwent more than 257,000 cycles of I.V.F. treatment between 2003 and 2010.

Researchers at the University of Bristol and the University of Glasgow defined a cycle as stimulation of ovaries to produce several eggs, plus all the resulting embryo transfers. These days, doctors are now encouraged to transfer just one or two embryos at a time to avoid multiple births. The rest are frozen for later attempts.

The rate of live births for participants after the first cycle in the new study was 29.5 percent, compared with 20.5 percent after the fourth cycle, 17.4 percent after the sixth cycle, and 15.7 percent after the ninth cycle.

“It’s never been shown in a large population before that that could be the case,” said Dr. Evan R. Myers, a researcher and a professor of obstetrics and gynecology at the Duke University Medical Center, who wrote an editorial accompanying the study. “Instead of saying, ‘If you haven’t been successful after three or four cycles, think about donor eggs or adoption,’ the study says, ‘If you keep going, there’s still a substantial chance.’ ”