Changing the login timeout for Windows Remote Desktop Services
After some more searching on Google, I managed to find a solution.
The login timeout is set in the registry, with the key HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Terminal Server\WinStations\RDP-Tcp
Simply add a new DWORD value for LogonTimeout, containing the timeout value in seconds. After that, restart the Terminal Services service. (If you are connected via Remote Desktop, your session will be terminated.)