I have a Kohler toilet (only about 2 years old) with the "silent fill" valve. When flushing, the float cup drops as the water goes out but then the refill does not start after it drops. If I apply just a little bit of downward pressure to the valve arm, moving it down just the tiniest amount further (like 1cm), it then starts refilling. I barely have to press it to get it unstuck. Even if all the water is out of the tank, it gets stuck, so it is not because the cup is floating on remaining water in the tank. I have tried removing/cleaning the rubber seal and flushing the valve with running water - that corrects the problem for a couple flushes, then it starts sticking again and I have to open the tank and lightly press the arm down to trigger the refill to begin. I've tried cleaning the shaft the float rides on, but can't find anything that would cause it to get stuck. The valve is at most 2 years old so it's pretty much "like new". Any suggestions, or should I just buy a new valve kit and replace it?