Outlook timeout while connecting to my IMAP account. What can I do to prevent this?

This is a known Outlook issue.  The Outlook program handles IMAP poorly, at best.  Thunderbird - or any other email program for that matter - does a much better job with IMAP.

And this is a result of the amount of email in your IMAP account growing large, and Outlook not being able to handle it properly.

Short of switching to a good IMAP email program, try the following:

• Click on "Tools", "E-Mail Accounts", "View or Change existing e-mail accounts".
•  Select your Brownrice Email account and click on "Change". 
• Click on "More Settings" and finally on "Advanced". 
• Change the "Server Timeouts" to the maximum (10 minutes) and click on "OK", "Next" and "Finish" to save your changes. 
• Exit and then restart Outlook.