Finder hiding is probably enabled. If the icons on the desktop disappear when an application is opened, Finder hiding is enabled. When Finder hiding is enabled, the Finder will hide (and the desktop icons will disappear) whenever you open an application.
To disable Finder hiding, open the control panel called General Controls and ensure that the button labeled "Show Desktop when in background" is checked. This disables Finder hiding. After disabling Finder hiding, the system will allow you to hide the open application.
Note that having Finder hiding enabled will only prevent the hiding of another application if that application is the ONLY other one open and not already hidden. Otherwise, everything could be hidden, and it stands to reason that this would present a problem.
If more than one application besides the Finder is open and Finder hiding is enabled, then all but one of the open applications will be able to be hidden. In short, there must always be at least one application, or layer, that is not hidden.