theme options not saving

Your register_setting() should be for all fields like below

function register_mysettings() {
  //register our settings
   register_setting( 'theme-settings-group', 'facebook' );
   register_setting( 'theme-settings-group', 'twitter' );
   register_setting( 'theme-settings-group', 'pinterest' );
   register_setting( 'theme-settings-group', 'googleplus' );
  //etc

}

Do this for all fields and let me know if you stuck at anything