Everyone seems to know that there's a kind of love/hate relationship between online radio listeners and the services that they use. It's great to have services like Pandora and Spotify, but trying to use a streaming service when away from home you have to either deal with WiFi (which has availablity and privacy concerns) or use a cellphone data plan which can have congestion issues, data caps and other issues of its own.
I have an answer if any of the services and the music industry have the guts to do it. On your mobile sevice, set up the service's app to automatically download x hours of music when it's docked or at home or connected to a wired network or whatever. The reccord companies are going to freak out about downloading and saving their music, so you just make sure the file is DRMed or encrypted so you can't access it except from the official app. That way it's no different than running the stream live, except that you're getting the stream at one time and playing back at another.