How do u Update previously purchased apps without having to sign in to billing

Is there a way to update ur previously purchased apps without having to sign in to billing? My credit card/debit card was stolen, so it's says that my payment method is declined, therefore I cannot update any apps (that require an update) thru my ipad2 or my IPAD 1. What f I decide to never use a credit card again? Does that mean I can't ever update any of my purchased apps? Especially if its an update that fixes some bugs or lagging, so I end up losing out?