The server is stopped.

When it shuts down, do you get an error message? Example: Lost Connection.

If you get the "Lost Connection" error, it might be your internet, if you use an wireless adapter, that might be the case. If you use ethernet cable, the cable might be broken/the internet crashes.

If none of the above apply, I reccomend you to do some tests, like changing the username, try testing the servers on other world(s) and things like that.