Frontend posting – everything saves other than checkboxes?

Did you check the database for the data?

My guess is that the problem is here:

echo '<input type="checkbox" name="cbn[]" id="'.$option['value'].'"',$checkboxes && in_array($option['value'], $checkboxes) ? ' checked="checked"' : '',' /> ';

should be:

echo '<input type="checkbox" name="cbn[]" id="'.$option['value'].'"'.$checkboxes && in_array($option['value'], $checkboxes) ? ' checked="checked"' : ''.' /> ';

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Edit:
You’re confusing poor PHP. Try enclosing the tertiary function in parenthesis.

echo '<input type="checkbox" name="cbn[]" id="' . $option['value'] .    '"' . ( $checkboxes && in_array( $option['value'], (array) $checkboxes ) ? ' checked="checked"' : '' ) . ' /> ';