We consider a two-player infinitely repeated game with asymptotically finite horizons:discount factors converge to zero over time. The stage-game has a continuum of actions anda unique and interior Nash equilibrium. It is known that when players perfectly observeeach other’s actions, cooperation can be achieved and equilibrium payoffs can be strictlyhigher than the stage-game equilibrium payoff. We show that introducing an arbitrarilysmall amount of smooth noise in the monitoring makes cooperation impossible and playersplay the static Nash equilibrium of the stage-game forever.