Check what you are doing to set up your desktop here: http://windows.microsoft.com/en-US/windows7/The-desktop-overview. Once you create your shortcut as shown it should stay on the desktop.
I have a new Dell StudioXPS 9000 with Windows 7. The desktop shortcut icons that I create myself to run existing programs keep disappearing from the desktop all by themselves. Those that were already on the desktop when I received the computer and those that are created by new software when installed on the computer have no problem remaining on the desktop. I never had the happen with WinXP. Am I doing something wrong?