Mine just started doing that 'flop down' thing too. I checked the tension cables and springs, they are OK, but there just doesn't seem to be the same amount of resistance on the 'flop over' part.
I think the springs are getting weak, but since you must drill out rivets etc to get to them, I think I'll just keep my hand on it so it doesn't flop.
Bottom line, she's getting old. ( aren't car years about the same as dog years ? )