@nayr I just finished adding SSL support into my mobile app and it also supports HTTP basic authorization. This should work perfectly with your proxy setup. I am using it with an Apache ProxyPass directive over SSL and Basic auth and it is working great!
The 401 status code cannot be detected on async AJAX calls with a timeout (because on mobile the authorization box is hidden but open until the timeout hits). Therefore, automatic redirection to authorization prompt is impossible. User may type user:pass@ip:port in the IP box however the user/pass becomes unnecessarily exposed. So I added a collapsible box with advanced options showing ssl and authorization (independent checkboxes). If you specify use authorization, a follow-up popup will show for the credentials.
I will post back here once the app’s are in the respective app stores with these features. Thanks for the motivation to secure things a bit!