This is commonly caused by something blocking your Messenger from getting to the internet. This could be a complete lack of internet connection, a firewall, or something else. Test getting online with Safari or another browser and ensure you're still connected
to the internet. If you are, ensure that any firewall software you have installed isn't preventing Messenger from connecting to the internet.
There's also a slight chance that the Messenger services were actually down at the time you tried to log in. You can check the current status of Messenger on the following link: