Well, I have always wondered why I have three or four IMAP logins for each user on my Mac OS X Server. This is covered pretty good on a NewGator discussion:
Mac Mail leaves one connection open for each IMAP folder, that is, INBOX, OUTBOX, TRASH, and any custom folders you may have.
So once users started getting iPhones and iPads in addition to their MacBooks, that number increased.
While not a great solution, it explained rather clearly to me what was going on. Hope it helps.
http://support.hostgator.com/articles/specialized-help/email/mac-mail-setup
The text part you want to read:
Too many [email] connections, 500 errors? Here is a fix.
Thunderbird is normally the route I suggest, however the main problem with Mac Mail I've seen is with the IDLE setting, basically this leaves the connection to the server open to check for new messages as soon as they arrive rather than trying to connect every say 5 minutes or so.
NOTE: Before this fix will work, you may need to kill your hanging processes. You can simply ask HostGator to kill all of your current processes.
This link describes the setting and how to change it in Mac Mail: http://email.about.com/od/macosxmail..._imap_idle.htm
And I'll copy the relevant parts here:
To have emails appear instantly in IMAP accounts in Mac OS X Mail:
Select Mail | Preferences... from the menu.
Choose Accounts.
Select the desired IMAP account.
Go to the Advanced tab.
Make sure Use IDLE command if the server supports it.
You can additionally uncheck Include when automatically checking for new mail. Keep in mind that Mac OS X Mail receives instant updates only for the open folder, though.
While this may be the desired affect, to get your emails instantly, Mac Mail leaves one connection open for each IMAP folder, that is, INBOX, OUTBOX, TRASH, and any custom folders you may have.
My simple suggestion: Turn off the IDLE function and set it to check every 5 minutes or longer, and monitor your connections.
