The news of Joan Rivers’ health fluctuates day to day, and while Hollywood and fans send their well-wishes on social-media sites, the family confirmed today that the 81 year-old comedian will remained on life support until further notice.

The confirmation was released earlier this afternoon (Tuesday) by Rivers’ daughter. Joan Rivers was hospitalized recently when she stopped breathing during a vocal cord procedure here in New York City.

In the same statement Melissa thanked fans and friends for their support during these trying times, saying that her mother would be grateful for the kindness that people have shown to her, and her family. Rivers has been under treatment at Mount Sinai Hospital since last Thursday.

“On behalf of my mother and our family, we are extremely grateful for all the love and support we’ve received. At this time, she does remain on life support,” Melissa Rivers said in a statement to the press sent out this afternoon.