My initial point was that since they are already using web technology they could probably move it to a web app for mobile outside the AppStore. But, as paulgb

My initial point was that since they are already using web technology they could probably move it to a web app for mobile outside the AppStore. But, as paulgb pointed out in another comment, Safari for iOS hasn't implemented push notifications from web apps which is probably a deal breaker for most users of an email app.