First it happened to my desktop and then my laptop. Re-installing or updating the messenger did not seem to solve the problem and it seems to happen randomly.

So I tried this solution.
WARNING: Messing with your registry can do some serious damage. So always be careful and back up.

1. Use “run” in the start menu
2. Type “regedit”
3. Open “HKEY_CURRENT_USER\Software\Microsoft\MSNMessenger”
4. Right mouse click on the key and export it to a folder (this is a back up)
4. Delete the folder called MSN Messenger
5. After this MSN Messenger Live will login as normal.

You will loose some of your customizations when you do this. So do take note.

My MSN Messenger works ok now. Cheers!