This problem occurs because in Internet Explorer 6 to 9 all style tags after the first 31 style tags are not applied. It includes inline CSS and loaded .css files. The solution is to decrease the amount of .css files the site loads:
- If you use W3 Total Cache, enable its CSS minify feature, to automatically combine multiple .css files into one.
- With Better WordPress Minify you can also achieve this just by having it installed, out of the box.