This property only reflects the state of client side of the connection. If the server forcibly closed the connection on its side, the application won't know about this until it makes an attempt to send or receive data.
In other words, it reflects the state of the connection at the time when the last data to the moment was received.
To check if you're still connected to the server from its point of view, issue a command to the server, such as Noop. If the method throws an exception, this means the server has closed the connection. If no exception occurred, the connection is still up.