Error 500? Too many connections. Here is the solution.
The problem is Mac Mail and the way it handles the connection.
Thunderbird is usually a better choice. The problem is with Mac mail and how it handles the connection with IDLE, leaving the connection open with the server to check for new messages, instead of connecting every 5 minutes.
NOTE: before this solution will work you should ask our support to close all the processes, the restart mac mail.
This link gives a better explanation: https://email.about.com/od/macosxmailtips/qt/et_imap_idle.htm