Perhaps you have an unusual pedaling style that tweaks your knee. A friend of mine that I tour with often rides with his knees out pretty wide and I have often suspected that is why he has endurance problems. In some of my photos of him I can see that his knees are out wider than his hands on his handlebars, his handlebars are the right width for his shoulders.

Any chance that you could get someone to ride behind you with a camera to make a video of your pedaling style so you can see if you are pedaling the way you should?