The skin.css file is created once the child cache folder is writeable, the first time you amend any Striking setting. So there is a permission problem at this moment. I think you should ftp to your site, and check the permission of your cache folder, which most likely should be at 777 or 775, depending on one's host.
But if I may ask, did you clear your cache in the Advanced Panel? You have to flush your cache as well, in order for the new cache to write.
Not only did I forget about that very straightforward solution Paul supplied (thank you Paul!), but I am thinking I need to check something in the child theme related to this topic.....
If you just create one and the goto the striking advanced section and import your striking settings from the correct theme then the skin.css is recreated with the correct settings.