Does your whole internet disconnect? Like you can't access websites, or just Messenger?
I need more information: If you say (!VER) in a conversation with someone (presuming you have Msg Plus! Live installed) it will tell you your Operating System, Messenger version and Plus! version, which helps us solve your problem. Copy and paste it to us.
Can you think of anything can could be blocking it? Like a firewall..? Which one do you have?
Are you directly connected to your modem or are you connected to the internet wirelessly through a router?
Have you tried testing your connection in Messenger? Go to Tools > Options > Connection > Advanced Settings > and click 'Test' on TCP. It should say 'Success'.
"Google is your friend." There are
many solutions to problems like this found on Google.