Paul Bettany, the actor behind Vision (and JARVIS), explained that it was (to him, at least) a thoughtless mistake.
He explained this to Entertainment Weekly
“You see him in the first movie, he’s born. He’s omnipotent, but he’s incredibly naïve. And in this movie he’s kind of beginning to take a more paternal role in the superhero family, and he’s growing at an exponential rate, and by the end of the movie he has a real emotion and real human reaction and he makes first mistake that he’s ever made.”
“What happened there is that his judgment was clouded there by real love and affection,” says Bettany. “And he responded in a quick and thoughtless way.… I really love that the moral compass of the movie is this synthetic person who’s trying to figure out what it means to be human. It’s a neat idea, you know?”
However, Bettany seems to be referring more to the fact that he fired the blast at all, something he knew was potentially lethal in a battle where everyone was pulling their punches. In the scene, Wanda had just been hit, and Vision reacts impulsively, missing and accidentally downing not only a friend, but a friend on his own side of the battle.
Why, specifically, he doesn't try to slow Rhodey's fall is left to interpretation right now, but Vision, who is becoming more and more human (including now beginning to fall in love with Wanda, who had just been hit), my guess is that he was stunned by his own actions and what he had done, and froze up briefly.