I had this problem recently too, and it took me a while to figure it out. In my case, and in the cases of several other posts I've seen, the issue was a bit of CSS code that Moodle didn't like. It was valid CSS, but Moodle can be picky sometimes. It's more forgiving in designer mode, which is why your CSS behaves correctly in designer mode but not in regular mode.
Try these things:
1. If you can, figure out which CSS sheet isn't loading. If you're very thorough in your testing, you can even figure out at what point the sheet stops loading. Moodle will load the sheet up until it encounters the error. Fix it and you're good to go.
2. If you can't find the problem, run all of your CSS through the W3C validator (http://jigsaw.w3.org/css-validator/) If there are any outright errors in your code, hopefully you'll find them then.
3. Eliminate any CSS shorthand. For example, instead of
border-bottom: 1px solid #E3E3E3; try
border-bottom-width: 1px;
border-bottom-style: solid;
border-bottom-color: #E3E3E3;
HTH,
Kimber
(Edited by Mary Evans - original submission Monday, 1 October 2012, 4:07 PM) Just added px to make border-width: 1px; as it was missing. 