There are several discussions on the web about technical details of how iOS 6 introduced a pain in the butt problem for us developer that when Safari's private mode is on, then the browser's LocalStorage is not writable.
But how are you dealing with this in your modern web application? Do you just detect this and notify the user via a modal window notification that your web application is not usable unless the user disables Safari's private mode? Or have you implemented fallback measures that don't use LocalStorage at all? If so, which measures are those?