How can I fix "Cannot open clipboard: Access Denied" errors?

I am using the following code to copy text to the clipboard:

  Clipboard.Open;
  try
    Clipboard.AsText := GenerateClipboardText;
  finally
    Clipboard.Close;
  end;

Seemingly at random I get "Cannot open clipboard: Access Denied" errors. I'm guessing that these errors are caused by other application locking the clipboard, but I never seem to be doing anything with other applications that should cause the locks.

Strangely my users seem to be reporting more of the errors with Vista and Windows 7 than with XP.

Is there a way to check if the clipboard is locked before trying to access it?