Strange. Have you tried to see if they might return after logging off and on, or restarting the computer?
Did you create the shortcuts directly from the game's EXE file?
Do you notice any pattern to when this happens? For example, after playing any games, or running any utility program.
You might also consider either creating a shortcut of the
hidden C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Games folder to the desktop, or
pinning this folder to the taskbar for a expanding Games folder to see how if it may work better for you until we can find out why the shortcuts are disappearing on you.