Asynchronous multi-direction server-client communication over the same open socket?

When I needed to write an application with a client-server model where the clients could leave and enter whenever they want, (I assume that's also the case for your application as you use mobile devices) I made sure that the clients send an online message to the server, indicating they were connected and ready to do whatever they needed doing.

at that time the server could send messages back to the client trough the same open connection.

Also, but I don't know if that is applicable for you, I had some sort of heartbeat the clients sent to the server, letting it know it was still online. That way the server knows when a client was forcibly disconnected from the network and it could mark that client back as offline.

Using asynchronous communication is totally possible in single thread!

There is a common design pattern in network software development called the reactor pattern (look at this book). Some well known network library provides an implementation of this pattern (look at ACE).

Briefly, the reactor is an object, you register all your sockets inside, and you wait for something. If something happened (new data arrived, connection close...) the reactor will notify you. And of course, you can use only one socket to send and received data asynchronously.

I'm not clear on whether or not you're wanting to add the asynchronous bits to the server in C# or the client in C++.

If you're talking about doing this in C++, desktop Windows platforms can do socket I/O asynchronously through the API's that use overlapped I/O. For sockets, WSASend, WSARecv both allow async I/O (read the documentation on their LPOVERLAPPED parameters, which you can populate with events that get set when the I/O completes).

I don't know if Windows Mobile platforms support these functions, so you might have to do some additional digging.