I can reproduce this on my Gentoo machine as well.
I did a patch a while back to remove use of deprecated ffmpeg functions and update to the new API:
https://developer.blender.org/D10338
It doesn’t apply to master, but if I roll back to a commit from the 8th of March (b1ef55abdbb9f47712049748ccf65d009c059160),
then it now prints an error message instead of failing silently:
Can't send audio frame: Invalid argument
It works with ffmpeg 4.3.2 but the latest 4.4 commit still fails, so if this is an ffmpeg issue, then they have not fixed it yet.
I also tried the ffmpeg master branch but blender will need more ffmpeg code cleanup as they have further enforced how they want you to use their API by declaring a few built in variables const.
(This breaks both our ffmpeg writer functions and the Audaspace lib we use for sound playback)
To figure out why it fails, we probably need to do a debug build of ffmpeg and blender and step through the code to figure out what the “invalid argument” is.
(I might be able to do this on monday, we’ll see)