Was not able to duplicate your issue locally, but was able to confirm using your site that profile update isn't working on your site for IE6, IE7, and IE8. Very likely a 3rd party JS conflict as the profile update button uses JS to validate the form before submitting. If there's a fatal JS error then that JS to submit the form will never execute. Please note JS is browser specific; this means it could work in FF, but not IE quite easily.
Please PM backend login credentials and will see if I can find the culprit.