Normal attack (right mouse click) doesn't always work

I did not set any action related to double right-click

I think that your problem is this. For some reason FROM decided that it is a good idea to use double-click as an entirely different category instead of just chaining a click. This means they need to detect the double-click, which persists even if you assign nothing to double-click. This moment of intelligence also blocks us from properly executing jumping strong attack (forward + strong attack at the same time)

This means that if you assign double-click to nothing and spam a click - hoping that finally the game will obey the common sense - the game will see you as initiating a double-click, sees that you assign nothing to double-click, and promptly does exactly what you told it to do: do nothing. It's not what you want it to do, but it's what it interpreted what you told it to do

You may want to check if your mouse's right click fires off in rapid succession with only one click, it might be the reason.

By the way this is also the reason I pretty much use keyboard keys instead of mouse clicks for my attacks. I assign the right hand normal attack to C and right hand strong attack to E