Parents of 545 children separated from their families at the border as part of the Trump administration's "zero tolerance" policy cannot be found, the American Civil Liberties Union says.
About two-thirds of the parents have been deported back to their country of origin, according to a court filing.
Thousands of families were separated under the 2018 policy, until the White House backed down amid an outcry.
The coronavirus pandemic has delayed searches for the still missing parents.
The crackdown on migrants crossing the US-Mexico border was first announced in April 2018, but it was later revealed that the administration had begun family separations a year earlier, as part of a secret pilot programme.
As soon as the zero tolerance migration policy was announced, pictures and audio emerged of children sleeping in cages and crying for their parents, provoking widespread criticism from within the US and around the globe.
In June 2018, in response to a suit filed by the American Civil Liberties Union (ACLU), a US judge ordered that migrant children and their parents be reunited within 30 days, and thousands of families were reunified within weeks.
But those separated by the 2017 pilot programme were not covered by this initial court order, and reunification of this group was only ordered last year. Of this group of 1,030 separated children, 485 have had their parents found.
The ACLU and a team of lawyers have been tasked with finding these parents, described as "unreachable" in court documents filed on Tuesday by the ACLU and the US Justice Department.
The group has conducted "time consuming and arduous on-the-ground searches for parents in their respective countries of origin", this week's filing says, efforts that have been obstructed by the coronavirus.
"People will ask when we will find all of these families, and sadly, I can't give an answer," Lee Gelernt of the ALCU's Immigrants' Rights Project said to NBC News on Tuesday.
"But we will not stop looking until we have found every one of the families, no matter how long it takes. The tragic reality is that hundreds of parents were deported to Central America without their children, who remain here with foster families or distant relatives".
The update on the search process was filed ahead of a status conference scheduled for Thursday before a federal judge in California.