Update 2. august 2010: There is a fixed RDM client for WM6.5 which is available to OEMs to include in there ROM images. Possibly you get it with an OS update of your device and will not see this issue any more. See also http://blogs.msdn.com/b/raffael/archive/2009/09/11/remote-desktop-mobile-rdp-client-disconnects-after-10-minutes-of-inactivity.aspx
Unfortunately Remote Desktop Mobile (RDM) Client, if part of your Windows Mobile 6.1 device, will disconnect after 10 minutes of user idle time. This value seems to be hardcoded into the application. Various searches in internet lead to this assumption. So regardless of your server or client settings, RDM will disconnect after 10 minutes of user idle.
The following code is from this blog. For those of you not being able to compile the code I have attached an ArmV4i executable you can use directly on your device.