To continue separating families, immigration agents appear to be taking advantage of a loophole in the court decision. The injunction doesn’t apply when parents have criminal histories or communicable diseases, which might require them to be quarantined away from their children. Nor does it explicitly apply when children are accompanied by relatives like siblings or grandparents rather than parents, unless those relatives are their legal guardians. And it permits family separation when a parent is deemed a danger to the child.

On the surface, these exceptions seem perfectly reasonable, particularly given the threat of human trafficking. But Enriquez, a lawyer, said they “left a big gaping hole that the government is driving a truck straight through.”

As part of the case the court ruled on, the A.C.L.U. receives lists approximately every month of separated families, with brief notations about the government’s justifications. Some of the misdeeds that are listed, said Gelernt, are extremely minor. For example, a 6-month-old was taken from his father because the father had a conviction for marijuana possession. Another dad lost his kid because he admitted to a conviction for driving with an expired license.

In some cases, the parents hadn’t been convicted of anything at all, but border agents claimed that they had gang affiliations. In other instances, agents stretched the definition of “communicable diseases” to apply to situations that don’t involve quarantine.

Gelernt described a case in which a Honduran man was separated from his three daughters because he was H.I.V. positive. (Their mother had died of AIDS.) Enriquez represented a child who was sent to New York after her mother was hospitalized for a leg injury in California. Even after the mother was discharged and released from immigration custody, Enriquez said, the government balked at returning her daughter to her until he threatened to sue.