Originally posted by @kewpie
It's not an automatic draw, because the game is still playable. It's up to the claimant to click the "claim draw" button when submitting the move. The only automatic draws are the ones where there is no possible move for a player whose turn it is to move.
Strictly speaking it should also be an automatic draw when there is no way either player can mate no matter how stupidly his opponent plays, but I believe that isn't currently implemented. It's in the FIDE laws, though.
(The list of those situations is small, by the way. It only happens when both players have bare kings, or both players have kings plus one bishop each and
the bishops are on the same colour squares, or one player has a bare king and the other only a king and either a bishop or
a knight. In all other situations, including when both players have a knight or when they have opposite-colour bishops, it's possible to help-mate.)
In fact, third repetition is needs to be claimed over the board as well. So does a fifty-move draw. The fifth-repetition and 75-move draws, both new since 2014, are I think automatic, but the arbiter would have to spot them happening to apply them against the will of the players, which I'm not sure has ever happened. In any case, at my own club I doubt there has ever been an occasion where those new rules could apply. They're there, AFAICT, only to prevent silliness.