I think that your problem is:
You have enabled the option "Allow automatic sign in when connected to the Internet" so, here is the problem: Your
disconnects, when the Internet connection starts again, messenger do an automatic sign in and the status is Online.
No need to Double Post, we are glad to help. Just wait.
By the way, Welcome to the Forums.
The "Allow automatic sign in when connected to the Internet" option is located at Tools/Options General Tab,