I think I'm starting to understand what's happening:

When the bug occurs, I can't send email with one of my 2 addresses for a
while.
Generally, the other address works fine, but not always.
After some hours, the bug goes away, without me doing anything special.

After reading through the auth-source manual, I realized thanks to
`(setq auth-source-debug 'trivia)' that the passwords are cached.

Running `(auth-source-forget-all-cached)' clears the issue instantly.

My conclusion is that somehow the password cache gets corrupted, in ways
that are not handled properly by Emacs.

What's really puzzling is that the issue is not deterministic.  The only
source of non-determinism I can see here is that the password cache is a
hash table.

Something else: I noticed that one of my passwords in .authinfo.gpg had
both a " (double quote) and a ' (simple quote), which, according to the
manual, is not supported.  auth-source does not catch this, it would be
nice if it would.

I've changed the offending password.  Let's see if I ever get an issue again.

--
Pierre Neidhardt
https://ambrevar.xyz/