The report problem seems to be cosmetic and I'm not sure yet how to best implement a fix, but I'm working on it.
I would like to resolve your main issue, the items not going out for 5 days.
What you report, that 5 days are sent in one shot, sounds like an SMTP queue problem. Perhaps your host has a hard time sending to certain domains and some messages (more and more, as the days go on) get left in the queue for extended periods of time causing a backlog.
The mail server can and should be optimized for large amounts of email to prevent queue problems. Suggestions for 'qmail' and 'exim' (cPanel hosts) server software are available in the forum - you might suggest those optimizations to your host.
Whether improvements to the config are made or not I would suggest that your host keep an eye on the outgoing queue over several days to see if it continually grows. Such activity can significantly slow down your outgoing email, as hard drive limitations with several thousand small files in a (few) folder(s) can quickly become an issue.
To prevent a backlog, the server should deliver all email as quickly as possible. It is recommended that your server be able to deliver the majority of messages as soon as they are queued by ListMail. There should only ever be a few thousand, at most, sitting in the queue for any length of time.
For your host's reference ListMail's mailing method is as such: Messages are sent over a single connection to SMTP.
Regards, DW