Microsoft appears to have released an update that deals with this problem: http://support.microsoft.com/kb/2721015
Specifically, MS says that:
| <ul><br><li>This update fixes an issue where some users who have IMAP accounts intermittently receive a “Too many simultaneous connections” error. A setting is now available to control the polling interval that Outlook uses with IMAP servers. <br><br><br><br>To adjust this setting, select <b>Tools</b>, select <b>Accounts</b>, and then select <b>Advanced </b>for the IMAP account. The setting defaults to synchronize all lMAP folders every two minutes. </li></ul> |
I updated MS Office on both my iMac and MacBook Air, and I didn't change the new default synchronization setting. The iMac only occasionally had this problem, and I cannot tell if the problem has gone away completely yet on that computer.
On my MacBook Air, I had resorted to deleting my Gmail accounts as I could access them via Apple Mail desktop application and I really didn't need Outlook functions with Gmail. I started to add back my Gmail accounts, but I was getting the error message
again. I turned off synchronization of IMAP folder while my mail downloaded, and the error message went away. After all my old email was downloaded, I turned IMAP folder synchronization back on (at the default 2 minutes).
It seems to have solved the problem for the most part. If you still get the error message, GMail folders may still be synchronizing, so you might have to keep hitting "No" a while longer until everything is synchronized.
So, with all due respect, it looks like it was a Microsoft problem after all. Fortunately I didn't try that time-consuming, tortuous fix recommended earlier.
I'll post an update on whether this fix has continued to work.