Ben,
Due to the server's 300 second time limit and your using the "bounce via mailbox" feature it's possible/probable that your dailymail script is timing out before getting to followup sending.
You will either have to disable bounce processing (make sure Admin email is on the ListMail domain for best results) or have your host increase or remove the script time limit.
You might also try running dailymail manually a few times with everything except "bounce via mailbox" disabled. (From within ListMail browse to the "Dailymail" page) This should clear out the mailbox which will shorten the time it takes to process future bounces.
Please let me know if I can be of further assistance!
Regards