The Audio Mixer will only save your changes if you adjust the levels as your video is playing. It can actually be a bit difficult to be precise with it.
A much more precise way to adjust audio levels is audio keyframing, in which you create keyframe points on your audio track on your timeline and you raise and lower audio levels at these specific points.
To create an audio keyframe, position the CTI playhead where you want to create a keyframe point and select that audio clip. Then click on the Make Keyframe button on the track headers, to the left of audio and video tracks.
It's much easier to describe with photos, and I do that in my books, available on Amazon.com and at the Muvipix store.