First, please make sure that the browser you are using is completely up to date. Using the latest version of your preferred browser is always recommended for the best and safest browsing.
If you are still having problems it may be because you have too many items in your closet. By default we limit closets to 650 items but you can remove this limit in your preferences page (http://www.neopets.com/preferences.phtml). Please try removing some of your items to give your closet an easier time loading. I know this isn't an ideal solution but it may help while we research a longer-term fix.
If all else fails it may help to use a different browser. We appreciate your feedback regarding customisation and I want to encourage you to submit an Ideas/Comments ticket about your experiences!