First off, open up Windows Live Mail, and then click on the Contacts tab at the bottom-left to open up your contacts.
Next, click on the "Export" tab at the top, and then click "Comma separated values (.CSV)"; when prompted, save the contacts.CSV file to any location, e.g. desktop.
Next, click on the blue Windows Live Mail drop-down menu icon (at the very top-left corner, above the 'Email Message' icon.)
Select 'Options', and then click on 'Mail' from the right.
In the Options window, select the 'Connection' tab and click 'Stop Signing in' under the 'Connecting to Windows Live Services' section. Click Apply > OK.
Done that, close and re-open Windows Live Mail - the error will have stopped coming up, but if you go to Contacts, you will see that your contacts have disappeared as well.
Next, in the Contacts window, click on "Import" at the top, and then click "Comma separated values (.CSV)".
When prompted, select the contacts.CSV file that you had exported earlier, and click Open. This will import all of your contacts back into Windows Live Mail (along with stopping the original error from showing up in the future as well.)