How many times can a monk use Deflect Missiles in a round?

Monks get the Deflect Missiles feature at 5th level.

How many times can a monk use Deflect Missiles in a round?

One of my players and I got into a debate. I contend that it is for one successful attack per round, while he maintains that it is more of a reaction and can be done as often as needed. Could someone please set us straight?