I can't reproduce the issue on iOS. In Safari it just shifts all the content up above the keyboard so you can always see the same content regardless of if the keyboard is open or not.
There is a problem in Chrome for Android, but it's not really a C2 bug, it's just an unfortunate consequence of the way Chrome handles the on-screen keyboard: when the keyboard comes up it actually fires resize events and causes the window size to change so it's reduced to just the area above the keyboard. Due to the fact you use "scale inner", this causes the aspect ratio to change, and then some text fields go off-screen so are hidden, and that causes the keyboard to be hidden if you tapped one of those text fields.
If you use letterbox mode it just scales down the entire view which keeps all the text fields on-screen and works OK. So really this is just a consequence of how Android handles bringing up the keyboard combined with the fullscreen mode you've chosen. It's similar to this bug, which Google are aware of and they plan to fix the keyboard to work like Safari to resolve issues like this. I assume it's a similar story on Windows Phone.
So closing as won't fix since it needs browser changes to work around. Alternatively you can just use letterbox scale.