Every time I switch my VirtualPC VM window between full-screen and windowed mode, it asks me to login. This is getting a trifle irritating and I can't understand why it does this. Can I stop it happening?
It's happening because you actually Remote Desktop into a MS VirtualPC.
With RDP, the video resolution is decided upon connection by the client, so to go to a different resolution in the client (like to full screen) it has to disconnect you, adjust the resolution in the client and then reconnect. And just like any time you connect via RDP, you need to give it credentials to log into a session (new or existing).
In the end I don't believe there's any way you can prevent it, short of changing to a different VM platform.