These keywords are hard to find on Google. But I found one link that talks about this problem.
https://community.spiceworks.com/topic/1995519-only-some-desktop-icons-disappearing-and-only-for-two-people
Desktop shortcuts disappear in Windows 7
https://support.microsoft.com/en-us/topic/desktop-shortcuts-disappear-in-windows-7-e6efbf49-ee07-a8e4-3d3e-cf27bb7c0b31
Summary
On your Windows 7 PC, shortcuts that you create on the desktop may be missing.
This can happen if the the System Maintenance troubleshooter detects the shortcuts as broken.
The System Maintenance troubleshooter performs a weekly maintenance of the operating system. The System Maintenance troubleshooter either fixes problems automatically or reports problems through Action Center. When there are more than four broken shortcuts on the desktop, the System Maintenance troubleshooter automatically removes all broken shortcuts from the desktop.What is a broken link?
A "Broken" shortcut is a shortcut to a file, folder or drive that may not always be available, for example, a desktop shortcut for a USB device may be regarded as broken if the USB device is not connected when the System Maintenance troubleshooter performs its maintenance, or, a network folder that is currently not available due to the network not being available.
Workaround
Method 1: Remove all broken shortcuts from your desktop
Keep the number of broken shortcuts on your desktop to four or less. You might accomplish this by removing all but 4 of your most used shortcuts on the Desktop. If have more than 4 shortcuts, you can also create a folder on your desktop and move the shortcuts to that folder. These shortcuts will not be removed since they don't sit directly on the desktop.
Method 2: Disable the System Maintenance troubleshooter
If you must have more than four broken shortcuts on your desktop, you can disable the System Maintenance troubleshooter.