This could be caused by a number of reasons beyond ListMessenger's control.
The first thing I would check is that you have appropriate entries for the "Messages Per Refresh" and "Pause Between Refreshes" settings in Control Panel, Preferences, Program Preferences. Make sure that you don't have ListMessenger trying to send too many messages per refresh or have it waiting too long between refreshes. I recommend the default setting of 75 messages per refresh or less and waiting 1 second before the next refresh.
This could also be caused by the setting in which you have ListMessenger sending mail. If the above settings are correct and you are still experiencing the problem, I would recommend changing the method in which ListMessenger sends mail. IE) If you're currently using PHP's mail() function, change to SMTP; if your using SMTP change to Sendmail; etc etc.
If problems persist, you can try asking in the forum.