One of our clients has had intermittent connectivity issues between Outlook 2010 and Exchange Online, and at first I thought it was just normal network blips causing them. We did put in a case during the first week, when there were ~ 20 users that lost connectivity at once, but then we never heard back. When the issues were ongoing, and appeared to be more frequent, I put in a new service request and called support. Initially, I was given some troubleshooting steps, nothing terribly useful, but then Monday a support engineer called and told me that this is a known issue that they are trying to fix. They actually applied a fix on Sunday, but we are still having issues, so I'm collecting data to send to them to help them pinpoint the issue.
I just wanted to put it out there that if you are having intermittent connectivity issues between Outlook and Exchange Online, delays in sending and receiving email, suddenly realizing that emails are stuck in the outbox, messages that Outlook is trying to contact the Exchange server, etc., put in a ticket with Microsoft. I'm sure that the more data they have, the better, and they need to be aware of the actual scope of the issue.