Doctors in a Florence, Ala., hospital continue to treat her for pneumonia and "they hope she'll improve," said Rob Laher of Tupelo.
Jones went on trial Oct. 1 in Booneville, accused in the 2010 shooting death of her mother, Jane Jones. A jury was selected a week ago and the trial got under way last Tuesday with opening statements and testimony from state witnesses.
But on Wednesday, Jones did not appear in court.
At that point, Laher told Judge Seth Pounds that his client was taken overnight to the hospital after she'd been found "unresponsive" on her home bathroom floor.
Pounds declared a mistrial and ordered Jones' arrest as soon as her health permits. He also ordered the district attorney's office to seek documentation about what caused her sudden illness.
Monday, Laher said Jones showed improvement over the weekend and briefly regained consciousness.
"She said she thought she was in a hotel - that she was late for court," he said.
But later in the weekend, her condition deteriorated and she was put on a ventilator to help her breathe, Laher noted.
Testimony at trial showed that Jones and her mother experienced years of discord, many believed to begin when Rebecca was 7 and with her 6-year-old sister at the bus stop when a school bus ran over the sister and killed her.
Last week, a medical examiner said Jane Jones died of a gunshot wound to the abdomen. She was pronounced dead at North Mississippi Medical Center.