Elizabeth Norton, historian and author of "Anne of Cleves: Henry VIII's Discarded Bride", writes of how Anne had been in ill health for some time when she was taken seriously ill at the end of April 1557. By 12th July she was bedridden and knew that she was dying and so made her will. It therefore was not a sudden illness.
Antonia Fraser writes "given the lingering course of the Lady Anna's illness, cancer seems a likely cause of her death. But no particular explanation was felt to be needed for the decease of a woman of her age" because Anne had exceeded the life expectancy of a Tudor woman. I too suspect cancer but, as Fraser points out, there is no way of knowing for sure because a cause of death was not given.