Irene Mayor was hospitalised in a critical condition after she was reportedly thrown into the air by the impact and landed awkwardly, breaking her pelvis and sustaining other injuries.
"Her age is a concern as far as the hospital is concerned," Irene's sister Joyce Shore told The Sun.
"Irene may not get through this," she added.
According to Joyce, Irene was a very active person prior to the accident. She enjoyed classic music and embroidery.
Earlier this week, Joyce told The Express: "I do like the royals, but the way my sister's life has been endangered is completely unacceptable. These outriders need to slow down.
"My sister is lying in a hospital bed and she could have been killed. She could so easily have been killed."
Clearly emotional, Ms Shore added: "But it will still go on. I doubt anything will change just because a lady speaks out over concern for her sister."
Meanwhile, William and Kate are said to be extremely upset about what has happened.
"The Duke and Duchess of Cambridge were deeply concerned and saddened to hear about the accident on Monday afternoon,’ Kensington Palace confirmed in an official statement.
"Their Royal Highnesses have sent their very best wishes to Irene and her family and will stay in touch throughout every stage of her recovery."