The cause described in the notification was :

error writing message: File too large

The first thing I did was checking my configuration file, main.cf.
It seemed all right :

[...]
mailbox_size_limit = 0
message_size_limit = 200000000
[...]

Note that “0” means unlimited.
I checked the mailbox in question : it was nearing the size of 50 Mb.

I started to think that during some Postfix update, the meaning of the value “0” may have changed.
I tried different values without success.

I started to become crazy with that, but, finally, after quite a long time spent on google, I finally found the trick, which is just a simple line to add in main.cf :

virtual_mailbox_limit = 0

Indeed, I use virtual users as mail account ! I just never imagined there was a differtent setting for virtual users (which can be a convenient setting in some case).