Washington (CNN) Supreme Court arguments Thursday on a case involving double jeopardy immediately turned heated, and Justice Ruth Bader Ginsburg was among the most relentless in questioning a lawyer at the lectern.

When another justice interrupted before the lawyer had finished answering one of Ginsburg's points, she did not give up.

"May I ask you to just step back so you can complete your answer to my question?" she said emphatically.

Ginsburg's message, explicit then, and implicit in other instances over the past month: I'm still here.

Since Ginsburg, 85, fell and cracked three ribs on November 7, there has been intense public scrutiny regarding her health and tenure on the nation's highest court.

She is the senior justice on the left wing, the leader of the resistance to the conservative majority, and, of course, the "Notorious RBG" icon whose life has been chronicled in film and books and whose daily ups-and-downs remain a staple of social media.

In recent years, her tendency to sometimes slouch in her chair or fall asleep, including at the State of the Union, has drawn notice. And for as active as she was on Thursday, she receded during Tuesday arguments in a patent dispute. She asked only one question and, with her head hung low, she was at times barely able to be seen on the tall mahogany bench.

A Ginsburg departure would give President Donald Trump a third nomination on the nine-seat bench and his first chance to replace a liberal with a conservative. During Barack Obama's tenure, Ginsburg resisted pressure to retire to give the Democratic president a chance to name her successor.

The potential impact of her retirement during the Trump presidency for the law in America cannot be overstated.

The public clearly understands that. News of her fall and cracked ribs -- at least the third such episode in the past six years -- made immediate headlines. "Get well" cards circulated digitally. People tweeted that they would give their ribs, and more, for her.

The justice, who was appointed to the court in 1993 and has been in the public eye since her women's rights advocacy in the 1970s, has responded with her own message of visibility -- to the extent she can.

She attended the funeral services for President George H.W. Bush at the Washington National Cathedral with all the other justices on Wednesday but passed up Tuesday's ceremonial arrival of Bush's flag-draped casket at the Capitol, an event at which the justices stood for the presentations.

In mid-November, she appeared at a White House ceremony for Medal of Freedom awards, where the late Justice Antonin Scalia, who was her best friend on the bench and who died in February 2016, was among those honored.

"Justice Ginsburg," Trump said, "glad to see you're feeling great."

Through her various falls and more serious health ailments over the years, Ginsburg has always made sure she was present for oral arguments, asking questions that demonstrated her deep knowledge of the of the case and law. Other justices often pick up on her lines of inquiry.

Ginsburg did not immediately respond to a CNN request about her health.

In 2009, a few weeks after surgery for pancreatic cancer, she showed up at Obama's televised speech to a joint session of Congress partly, she said, because she wanted people "to see I was alive and well, contrary to that senator who said I'd be dead within nine months." Sen. Jim Bunning, a Kentucky Republican, had predicted that she could die from the pancreatic cancer within nine months. (Bunning, who later apologized, died in May 2017.)

During Obama's second term, she brushed aside comments that she should retire, to give the Democrat a chance to make a new Supreme Court appointment. She insisted her tenure would not be tied to the politics of the day.