Managing blocks in a responsive theme
I can't go into a lot of details, as I've not used either module for ages (I build all my sites with Context from the word go and I've not picked up responsive on something I haven't built for a while, so I've not had this problem before), but I think you should be able to put something together with Mobile Tools and Spaces. 

Spaces


  Spaces is an API module intended to make configuration options generally avaliable only at the sitewide level to be configurable and overridden by individual "spaces" on a Drupal site. It has been described as:
  
  
  A way to make one Drupal site act like several sites
  A way to provide much more configurable, full-feature Organic Groups or user homepages
  A generalized API for contextual configuration
  


Mobile Tools


  The Mobile Tools module provides Drupal developers with some tools to
  assist in making adjustments to your site based on the visitor's
  device.


The project page for MT does say it's not ready for production though, which might be a problem - it depends when  it was last updated, as the last commit was this month.

*EDIT

I COMPLETELY FORGOT ABOUT THESE!

Browscap


  Browscap provides an improved version of PHP's get_browser() function.


Browscap block


  Browscap Block adds visibility options to block configuration settings
  to allow you hide or show blocks in mobile devices.


Browscap does depend on your server setup, but if you can use it then the second module gives you extra visibility settings for each block on the block edit page.