It can mean that their email servers are either down or that you are logged into their webmail at the same time or have been recently and haven't logged out fully yet. It can also occur if you need to retype your username and password in again. Have you tried to see if you can login using your details on O2's Webmail service? I'm not 100% sure whether they've linked it to broadband accounts yet but I'd assume so.
Otherwise you might want to consider trying a different e-mail software, such as the excellent Thunderbird just to test with something else. I eventually had enough of Outlook and moved over, haven't been happier since.
Mark 'Winter' Jackson
Editor-in-Chief - ISPreview.co.uk