Fair catch?

Joe Root (124) shared a stand of 179 with Moeen Ali (99no) in the First Test Match in India. He barely put a foot wrong until he drove a low catch straight back at Umesh Yadav in the evening session and departed. The bowler threw the ball in the air but tried to catch it again and missed it. After a third-umpire consultation which provided an additional talking point, to a fine-margin decision that the bowler had the ball under control before dropping it again in a faulty celebratory juggle

The relevant clause in Law 33.3 and states "The act of making a catch shall start from the time when the ball first comes into contact with a fielder’s person and shall end when a fielder obtains complete control over both the ball and his/her own movement."

The fielder had control of the ball because he was able to throw it in the air. He doesn't have to catch the ball again when it comes down

Read more about Law 33 (Caught) at the MCC website