A recent result in reputation games is that after an arbitrarily long history, any equilibrium of the continuation game must be an equilibrium of the complete information game. We show that for a particular class of games, this result assumes that the uninformed player has infi…nite memory. In fact, we show that if the game is sufficiently noisy, a bounded memory player may never be able to learn anything at all. Our result implies that bounded memory can be an explanation to long-term relationships, even in the extreme case of parties with zero-sum preferences.