I have 2 guesses.
One is that the clip in the bottom of the socket that provide the 12 volts has loosened up so it won't contact your lighter or radar detector power lead. This would seem logical given that you state the 12 volts is actually present in the socket.
Another possiblity is that when you tested for 12 volts, you used a ground other than the outer shield (inside the power socket for the lighter) and that in fact there is 12 volts present, but not a ground.
Are you testing it by inserting the tip of the positive lead on your meter to the bottom center of the plug, and the gound lead to the inside of the socket along the side wall?
If the clip that has the 12 volt power has loosened up, you can tighten them up again with a screwdriver if you first remove the fuse, or with a non-metallic object such as a plastic wedge.