Any Internet connection should be sufficient, however you say you are using public wifi spots, these usually require you to open a webpage and fill out a form of some kind in order to connect to it, as the RC2 doesnt have a browser then this may...
Strangely its been 13 months since i purchased my Mini 4 pro and have yet to have to login to the app since my first login, I have the RC2 if that makes a difference
It sounds like your RC2 is failing to get internet access,
Not sure what you mean by this, but here are my suggestions apologies if its something you have already tried.
To access Your internet connection swipe down from the top of the screen...