I've gotten the Knight's responsiblity to duel the challenger several times and had no problems with it, but now in a new kingdom it just doesn't work. He duels her and beats her (and I know from my previous times doing this responsiblity that he shoudln't have to beat her anyway), but the responsiblity is still there counting down. I have tried quitting and reloading the game, but the same thing happens.

Has anyone else had this problem? Is there a solution to this? Any suggestions?

I think you have to build up your knights strength right in the beginning, like by using the training dummy. I usually let the first couple of days responsibilities lapse since a lot of them can't be completed when the hero is at the lowest level.

...but he duels her and beats her. It is in no way a lack of strength on his part.

I have played a level 1 Knight several times and I have never had to let any responsibilities lapse.

I am having the same problem and it is the first time it's happened to me. I know I'm doing it right. My knight is Level 4 in his profession. The only thing I can come up with it's a glitch or bug. The only thing I can do is take the negative bluff which sucks monkey butt.