Maybe you've hit the notorious limitation of Internet Explorer - it can load up to 32 CSS files and if there are more, they will be ingnored. This problem can occur in case you are using a theme with a lot of CSS (when you register the theme, automatically all the CSS is declared) or you have declared a lot of RadControls on the page. If you are using a theme you can test my assumption by removing it and test whether the RadTabStrip CSS will load correctly.
If this is the case I suggest to either use a RadStyleSheetManager which will combine all the CSS on the page or reduce the CSS files used.
All the best,
the Telerik team