FIDE laws of chess: The game is drawn upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by a repetition of moves)
It is repetition of position not repetition of moves that counts.
However according to the FIDE laws, you have to claim before you make your move, could this be why the draw didn't happen?
On this site there is no arbiter so the player makes the move then tries to claim the draw before his opponent spoils the position by making a move.
http://support.chess.com/Knowledgebase/Article/View/40/0/how-do-i-claim-a-draw-in-live-chess
"Once the position has repeated three times, make your move then click on the "Draw" button. This ends the game as a draw."
It's not a draw, because white's move at 55. was a pawn move.