The Delete key does not delete Key Frames never has. You have to use the + and - buttons in on the animation toolbar. If you use the one on the Pose window then it adds and deletes all key frames on all items. Using it on the animation palette you can choose to have it effect everything or just the currently selected body part. If you have it set to selected then you can collapse a body part down and delete Key Frames for everything on the part (which could the body which removes all Key frames for a single figure but leaves the other figure along).

Poser 5, 6, 7, 8, Poser Pro 9 (2012), 10 (2014), 11, 12, 13