What was the reason for O'Brien to leave the series Downton Abbey with no explanation?
It was explained in the show. She decided to become lady's maid of Susan MacClare.
It was in the first episode of the fourth season (I don't remember if it was shown or only mentioned).
From her page on Downton Abbey Wiki:
In February 1922, she sneaked away in the night to travel to India to be a lady's maid to Susan MacClare, Marchioness of Flintshire.
Later we find out that she made a career in India:
According to Mrs Hughes, by 1924, Miss O'Brien had been employed by the new Governor's wife in India.