As far as I'm aware, the plugin isn't doing anything that would result in limiting the number or rate at which you can post emails.
The first thing to do would be to log into your email account directly and verify that all the emails are showing up in the inbox. There are many places that could be introducing a delay here, from limits on your SMTP service queueing messages to limits on your receiving mailbox.
If they're in the inbox and not getting posted, try to figure out whether it's the *same* emails that aren't getting posted each time (which would indicate the plugin might be having a hard time parsing those emails for some reason) or if it really is a maximum number or rate. It might help to enable WP_DEBUG and see if any errors are displayed when you check for new mail. You can also look at your Apache error log and see if anything is showing up there.
It's possible that trying to load a bunch of emails at once is causing the plugin to run out of memory -- so please do let me know what you find out.
All of that being said, I'm not convinced that the Post By Email plugin is the best way to accomplish what you're trying to do. It might be far easier and less error-prone to convert all your existing posts to e.g. CSV format and import them directly into your WordPress site. There's a lot of information on importing from various formats on this Codex page.