A solução é que a equipe do sendmail examine seu arquivo "/etc/mail/sendmail.mc":
dnl #
dnl # The following limits the number of processes sendmail can fork to accept
dnl # incoming messages or process its message queues to 20.) sendmail refuses
dnl # to accept connections once it has reached its quota of child processes.
dnl #
dnl define('confMAX_DAEMON_CHILDREN', '20')dnl
dnl #
dnl # Limits the number of new connections per second. This caps the overhead
dnl # incurred due to forking new sendmail processes. May be useful against
dnl # DoS attacks or barrages of spam. (As mentioned below, a per-IP address
dnl # limit would be useful but is not available as an option at this writing.)
dnl #
dnl define('confCONNECTION_RATE_THROTTLE', '3')dnl
(Treat "dnl" as a comment leadin string.)
Se você está apenas enviando os e-mails para fora, provavelmente deve controlá-los.