I had the same problem- key bindings worked on training missions and did not when i tried to play any other mission. In my case helped changing settings; go into setting and at the top you have some tabs like controls and gameplay. Even if you bind your keyboard and joystick to sim mode in "CONTROLS" you still need to go to "GAMEPLAY" and tick/untick two top boxes on the left, named something like "game style avionics" and 'game style flying"- if i remember correctly. You may also want to adjust some other options from this tab, but those two I think are necessary for the plane to work properly. At least in my case that worked