This TechNet thread illustrates the user community investigation process. The threshold to trigger shortcut removal seems to be more than 4 shortcuts to unavailable files/folders.
LifeHacker covered the problem back in March 2010, with a rather arcane introduction to editing the scripts that control Win7 system maintenance. Basically Win7 withholds edit privileges on the relevant script, so the first task is to "take ownership" (computer admin lingo for elevating user privileges to override system protection). The Lifehacker article supplies a broken link to a SevenForums article in the body, but provides a linked reference to a gHacks article at the end, which in turn provides a working link to the SevenForums article that provides a "take ownership" Explorer context menu item.
Then we navigate via Explorer to C:\Windows\diagnostics\scheduled\Maintenance, and take ownership of TS_BrokenShortcuts.ps1 and TS_UnusedDesktopIcons.ps1.
Then we right-click a command-prompt icon, Run as Administrator, and paste the following commands to assign file-save rights to the current user:
icacls c:\windows\diagnostics\scheduled\maintenance\TS_UnusedDesktopIcons.ps1 /grant USERNAME:F
icacls c:\windows\diagnostics\scheduled\maintenance\TS_BrokenShortcuts.ps1 /grant USERNAME:F
...replacing "USERNAME" with your username, of course.
In TS_BrokenShortcuts.ps1 we delete everything between [string]$list = "" and return $list, approximately lines 12 to 21. In TS_UnusedDesktopIcons.ps1 the same lines bracket the portion we want to delete, approximately line numbers 25-34.
Incidentally, the .PS1 extension signifies the PowerShell language, an extension of the command-line scripting language we've been using for shell scripting since before Windows. icacls is the current Windows generation's implementation of cacls, the Command-line tool for editing ACLs (Access Control Lists) - basically a filesystem user-level security twiddler.