Thank you for the answer.
Want to share solution that I’ve found for the issue.
During investigation I noticed that css file (Window.ThemeName.css) loaded correctly, but skin images are not loaded. And this happens from time to time for all browsers (IE, Chrome, FF).
So I have replaced image links with inline base64 encoded strings in the css file and the issue has gone!
Here is link to the online tool to convert images to encoded strings http://webcodertools.com/imagetobase64converter