You say you cannot pin it but then show you have, albeit not with full functionality. It works as expected on the machines I have looked at so it might be worth deleting this icon and trying again.
If you right click the icon in the start menu, there should be a Pin to Taskbar option. Try that.
See www.grainge.org for RoboHelp and Authoring tips
It's a Windows thing: you're not allowed by default to pin items with
Help in the name to the taskbar.
There are two solutions:
Change your shortcut name. See
Change your registry to remove this limitation altogether. See
Thanks, William. I renamed the shortcut and I was able to pin it. And I can open more than one window from it.
That restricted list for pinning has to be the most ridiculous Windows quirk in a long time.
It's a strange quirck. It is removed in Windows 8.1. At least, there I
can pin RH to the taskbar without a problem.