He's entitled to play on if he wants to .. I expect he thought he might be able to manouvre for a skewer or something. Now if you'd been rated say 1600 he probably wouldn't have bothered 
dead draw
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In this game http://www.chess.com/livechess/game?id=705689154 we both had 1 rook from move 83 till the end move 105.My opponent didn't accept my draw offers.