Essentially, inetd is getting more requests for the auth service than it has been told to handle. The auth service is handled by identd on my box. Why the problem occurred I noticed that the problem was occuring during times of mailing list activity. When the mail server was going flat-out trying to deliver mail, the error message would occur. I could easily see that when the mail messages started flowing, the auth requests started as well.
Most mail servers act that way.
They use auth as part of the security check. What didn't work This bit didn't work. Don't do this. But after about ten minutes, the problem returned. The problem did not recur.