What i remember from the Erlang discussions around Whatsapp, they dont keep the messages on the server, only temporary until it has been delivered. So Im guessing that is the reason why they need your phone to be connected.
Might have been in this video [1]... Not sure at the moment (will check later when im out of the office).
"What protocol is used in Whatsapp app? SSL socket to the WhatsApp server pools. All messages are queued on the server until the client reconnects to retrieve the messages. The successful retrieval of a message is sent back to the whatsapp server which forwards this status back to the original sender (which will see that as a "checkmark" icon next to the message). Messages are wiped from the server memory as soon as the client has accepted the message"
Might have been in this video [1]... Not sure at the moment (will check later when im out of the office).
[1] http://vimeo.com/44312354