Connie Yates and Charlie's father Chris Gard on Monday gave up attempts to persuade a judge to allow their 11-month-old son to travel to America for experimental therapy.
But the judge who analysed the litigation was overseeing a further hearing in the case on Tuesday afternoon at which the parents' wish to take their son home to die was being discussed.
Ms Yates arrived at court shortly before 2pm.
The couple on Monday said they wanted to "spend our last precious moments" with Charlie and Ms Yates said she did not expect her son to live until his first birthday on August 4.
Great Ormond Street Hospital officials have not said when Charlie's life support equipment will be turned off.
But in late June, when litigation appeared to have come to an end, a hospital spokeswoman had said there would be ''careful planning and discussion'' before life-support treatment ended.
Mr Gard and Ms Yates, who are aged in their 30s and come from Bedfont, west London, had asked Mr Justice Francis to rule that Charlie should be allowed to undergo a therapy trial in New York.
Doctors at Great Ormond Street said the therapy would not help. They said life-support treatment should stop.
Mr Justice Francis in April ruled in favour of Great Ormond Street and said Charlie should be allowed to die with dignity.
Charlie's parents subsequently failed to overturn his ruling in the High Court, Court of Appeal and Supreme Court in London.
They also failed to persuade European Court of Human Rights judges to intervene.
But the couple had recently returned to court, saying they had new evidence and they asked Mr Justice Francis to change his mind.
But the couple abandoned their legal fight on Monday after concluding that Charlie had deteriorated to the ''point of no return''.