“Is anybody overseeing devices like this?” said Dr. Gayle S. Smith, a pediatrician in Richmond, Va., who said she had treated a Brezza-fed baby for failure to thrive. Or, she added, “is it babies who are supposed to fail to thrive in large enough numbers” before regulators intervene?

Mr. Contract said the machines were safe and met F.D.A. requirements for materials that come into contact with food.

Dr. Jacqueline Winkelmann, a pediatrician in Orange, Calif., said she had seen babies admitted to a hospital for weight loss because they were given bottles that had been mixed incorrectly by hand.

“I believe the Baby Brezza Formula Pro is a great way to ensure baby gets the right amount of nutrients in every bottle,” said Dr. Winkelmann, who consults for the Betesh Group.

The Betesh Group began selling automated formula-dispensing machines in 2013. The devices took off in 2018 when the company introduced a new model, the Baby Brezza Formula Pro Advanced. About half a million of the Brezza machines have been sold in the United States, the company said. Several similar machines are also available, with brand names like Baby EXO and Zomom.

To use the Brezza machine, people fill compartments for water and infant formula powder. They also set the machine to their desired number of ounces and specific type of formula. Mr. Contract said the devices can save parents several minutes per formula bottle, a welcome convenience in the middle of the night.

On BabyList, a popular site for expectant parents, more than 60,000 people — or about 6 percent of users — included the Brezza machines on their baby gift registries last year. Many parents swear by the devices.