Yes, I have that problem, too. The issue on my lamp is that the connector to the arm (i.e. the rivet) should be in a fixed position. There's an additional friction mechanism in closer to the red isolating plastic piece that allows arm adjustment when in use. Because the connector moves freely now, it falls down. I called the company (no answer to support line). I emailed them, but got only one reply saying email another address, which did not reply at all. TERRIBLE CUSTOMER SERVICE. The fix I made was to epoxy the connector/rivet to the arm. Be sure not to epoxy the internal friction point. I'd put a picture here to show you, but this system doesn't allow.
Preston, November 2012