They have a software update for them. Go to http://worldwide.bose.com/downloads/en/web/soundlink_mini_ii_webapp/page.html#section=install
download it and fallow the directions, it will update your unit and the problem will be fixed. It enters shipping mode if its not turned on for a wile. I have the same speaker and had the same problem. Did the update and its all good now. Mine updated from 1.1.3.something to 1.1.4.something
good luck
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F.Y.I. Software updates are only available for the SoundLink Mini II (not the first version). Updating/downgrading the software seems to be a common fix for the Mini II, but for the first generation Mini you can see a list of common problems and solutions on this page: [https://www.ifixit.com/Wiki/SoundLink_Mini_Won%27t_Turn_on_When_Connected_to_Power|SoundLink Mini Won’t Turn on When Connected to Power]
They have a software update for them. Go to http://worldwide.bose.com/downloads/en/web/soundlink_mini_ii_webapp/page.html#section=install
download it and fallow the directions, it will update your unit and the problem will be fixed. It enters shipping mode if its not turned on for a wile. I have the same speaker and had the same problem. Did the update and its all good now. Mine updated from 1.1.3.something to 1.1.4.something
good luck