Is there any way to avoid losing a generation of quality when re-exporting an .mp4 after making changes to it?
@user2248 is on the money. The only software I know of that can do this sort of thing is ffmpeg. I'll expand on his answer:


Import mymovie.mp4 into Premiere Pro, or audition or whatever.
Do your sound edit, and export just the audio to myfixedaudio.wav (or .aiff). 
Now comes the scary command line stuff:




ffmpeg -i mymovie.mp4 -i myfixedaudio.wav -c:v copy -map 0:v -map 1:a myfixedmp4.mp4


Wow, a whole line of typing, that's going to take forever. Seriously, it might seem that it's mysterious and difficult, but it's actually less work than doing it with the GUI. let's break down that command so you can see what it's doing:


-i mymovie.mp4 -i myfixedaudio.wav import the movie, and the audio. FFMPEG numbers from 0, so mymovie.mp4 is source 0 and myfixedaudio.wav is source 1
-c:v copy set the codec for video to copy, aka completely lossless copy of the original encoded video, copied bit for bit. We don't need to set the codec for audio because it sets the appropriate audio codec for mp4 by default (aac).
-map 0:v -map 1:a map the video from the first source and the audio from the second source to the first and second streams of the output. I.e. the output now has an identical video stream to the original movie, and a re-encoded audio stream from the fixed version in the wav file.
myfixedmp4.mp4 ffmpeg uses the first thing it sees as a filename without a -option in front of it as the output.
if you wanted to preserve more audio quality, you could muck around with the audio settings, you'd do that before the output name.


Compare that to what you'd do in Premiere:


import the movie and the audio
create a new timeline
add the just video to the timeline by deactivating the audio and then dragging the video into the timeline, or by selecting the original audio track from the movie and deleting it
add the new audio
export the movie, after adjusting the export settings


Same same, only you do it with a lot more clicking and dragging and keystrokes. Not to mention that it can't actually do what ffmpeg can.

This will not preserve your audio losslessly, but nothing will. It will however avoid a generation loss with your video, and it is the only way I know of that will.