It is somewhat 'ticklish', right enough! However it does work. When you click (and hold) on the layer look for the black line. You may need to move your cursor a little to the left to actually see the black line under the blue high-light bar. As you drag the layer up and down, the blackline should follow and indicates where your layer will end up. If you pause on top of another layer or too far beyond the start/end of the layer list, the black line will dissapear. If you cannot see the black line, your layer will not be moved.
If you are using an old version of QGIS (pre 2.0) then you may need to set the 'update drawing order' flag. Do this by right-clicking on the layers list and you'll find it. This option does not exist in the most recent versions of QGIS because the update is automatic (so this comment is only for other readers with older versions).