The shutter speeds you state are probably too low to handhold a camera when the lens is zoomed to telephoto. The old rule is to not attempt handholding a camera when the shutter speed is below that of the focal length of the lens, e.g. one should not attempt a handhold of a 100mm lens below 1/125 of a second and so on. To get around this you could increase the ISO, or use a tripod. Pardon me if this is old material, however I did not see a reply to your post.