I'm having the same issue. This thread was started in April. It's July and there still is no solution. What's up with that??
I just received an official response from a Microsoft Senior Support Engineer acknowledging that it is a Microsoft problem. It doesn't mention that the last Service Patch from Microsoft was the culprit (it was), but It says:
Hi Steve,
It was my pleasure to assist you with this case. I am providing you with a summary of the key points of the case for your records. If you have any questions please feel free to call me; my contact information is listed below.
Based on our last communication, it appears that this case is ready to be closed. If this is premature or if you need additional assistance with this case XYZ, please let me know as soon as possible.
Thank you for choosing Microsoft.
Symptom:
Error message in Outlook 2011 “Mail could not be received at this time. The server for account “Gmail” returned the error “[ALERT] Too many simultaneous connections. (Failure).” Your username/password or security settings may be incorrect. Would
you like to try re-entering your password?”
Cause:
This error occurs because of an IMAP connection limit imposed from the Gmail servers and the way Outlook 2011 is using IMAP connections to the server.
Resolution:
This is a known issue that Microsoft is currently working on. The anticipated date for release of this fix is the end of July, pending the completion of the fix and the applicable testing.
Since this is a known issue, I will close this case as we agreed with the understanding that you will not be charged for this incident.
Senior Support Engineer, Microsoft Office Support – Outlook | Microsoft Corporation