Debra Sukin and her husband were determined to take no chances with her second pregnancy. Their first child, Jacob, who had a serious genetic disorder, did not babble when he was a year old and had severe developmental delays. So the second time around, Ms. Sukin had what was then the most advanced prenatal testing.

The test found no sign of Angelman syndrome, the rare genetic disorder that had struck Jacob. But as months passed, Eli was not crawling or walking or babbling at ages when other babies were.

“Whatever the milestones were, my son was not meeting them,” Ms. Sukin said.

Desperate to find out what is wrong with Eli, now 8, the Sukins, of The Woodlands, Tex., have become pioneers in a new kind of testing that is proving particularly helpful in diagnosing mysterious neurological illnesses in children. Scientists sequence all of a patient’s genes, systematically searching for disease-causing mutations.

A few years ago, this sort of test was so difficult and expensive that it was generally only available to participants in research projects like those sponsored by the National Institutes of Health. But the price has plunged in just a few years from tens of thousands of dollars to around $7,000 to $9,000 for a family. Baylor College of Medicine and a handful of companies are now offering it. Insurers usually pay.