EZ, we may have had a little misunderstanding. I was assuming that the ~ 1" black knob had broken off, resulting in a leak - if that's the case, my advice on the screw will stop the leak. Is the black rubber 'shaft' still sticking out of it? (it's really small) If it is, don't do the screw thing unless the leak is large or you have no hope of finding a replacement 'lube knob'. (I believe I have a couple on our service van that we salvaged from a replumb).
As for how often to lube it, whenever the valve becomes hard to turn.