Video Degradation ...

I have a handful of musical MP4 videos that; (i) are losing picture quality, and (ii) losing sync between the music and the artist's performance. Why does this happen over time and is there anything I can do to prevent this?
Are these videos that you created - or perhaps all videos are from one source?

try IINA.
This is a recently developed video player, and updated frequently. It might help your sync issues.
Many thanks. I have downloaded IINA. A very good player but it has not resolved the sync issue. Curious problem overall (but not a dire emergency!).
Still out of sync after a fresh restart of your system?
Is the audio out of sync immediately, or after playing for a minute or two?

And, my other question, too.... Are the videos from only one source, and did you create them?
Do other video types also go out of sync (or only MP4 videos?)
The out of sync is immediate DeltaMac. The few MP4 videos I have are all from YouTube. Apart from one movie, they are music videos and the loss of sync is very subtle. However I have a lengthy non-music MP4 movie of a pilot's cockpit view of a landing. The pilot's voices are both 10 seconds late after you see their lips move! Of course this is not affecting the quality of my life (first world problems etc). I am just curious to know how this loss of sync has developed over time compared when I first viewed these videos months ago.
Youtube videos?
Are those videos that you uploaded to YouTube, and now won't stream properly.
Or videos that you downloaded from YouTube, and the files that you downloaded now show that out-of-sync ...
Do you get ANY improvement after you restart your Mac, then immediately try your video?
If you stream those videos (try the worst one first) direct from Youtube, do you still have the sync issues, even from that original video?

As there are many sites that report problems with video/audio going out of sync, both Windows and other operating systems, you may have an issue that does not have an easy answer.

I would suggest that you can try dragging your user (home)/Library/Caches folder to the trash, then restart your Mac. There may be some odd cache file connected with video play that is corrupted in some way. Removing the entire Caches folder, then restarting (the folder will rebuild as needed) just might take care of your issue, if it is a user issue.
You can also try your video after logging in to another user account. If you get normal video play, then it may be something else in your normal user folder.