I always hear this but no one ever tells me just what precedents for robotic warfare they find troubling.

It is a further dehumanization of the process of killing and so tends to undermine any inbuilt human moral repugnance produced by violence. To the extent that you think that killing humans is a bad thing I suggest that is something that should be of concern. It is one more level of emotional detachment for the drone operators beyond what can be observed in the Apache pilots in the recent Wikileaks collateral murder video.

ETA: This Dylan Rattigan clip discusses some of the concerns raised by the Wikileaks video. The same concerns apply to drone attacks, only more so.