I have seen this bug happen several times in the past few days - on 2 seperate computers - and I have never seen it before.
What happens:
-card starts to draw, you can see what it is going to be and just disappears. It does not appear in your hand. It does not end up in play. If you click where it would be, you get nothing (aka it is not invisible)
-I have not "clicked" anything when it disappeared (different from OP).
-I've had it happen early in the game and so I could count my cards backwards, it most definately is disappearing.
It is completely game breaking when it happens to a key card in your deck.