The fix seems to be very simple:

diff --git a/Lib/mailbox.py b/Lib/mailbox.py
index a677729..2be4c83 100644
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -675,6 +675,7 @@ class _singlefileMailbox(Mailbox):
                     new_file.write(buffer)
                 new_toc[key] = (new_start, new_file.tell())
                 self._post_message_hook(new_file)
+            self._file_length = new_file.tell()
         except:
             new_file.close()
             os.remove(new_file.name)

I guess all single-file mailboxes have this issue, not only mbox. I'll still need to add tests when I have time.