As @Raphael said, editing /etc/exim4/exim4.conf.template and adding directive smtp_accept_max = HereTheNumber must work, maybe you should raise another smtp_accept limit.
If you want to check the current values used in your Exim service:
The non-mail SMTP commands are those other than MAIL, RCPT, and DATA. Exim counts such commands and drops the connection if there are too many of them in a single SMTP session.