Submitted for Review back to a Draft page

This is not a permissions issue – contributors can (by default) change a post from pending to draft. To test, submit a post for review, then “quick edit” it – you’ll see that you’re able to change the status back to draft.

The issue is that the “save as draft” button in the UI is hidden once a post is submitted for review – let’s “restore” it:

function wpse_210259_revert_to_draft_button() {
    global $post;

    $post_type = get_post_type_object( $post->post_type );

    if ( $post->post_status === 'pending' && ! current_user_can( $post_type->cap->publish_posts ) ) {
        printf(
            /**
             * Since there are no hooks where the original "Save Draft" button
             * appears, use CSS positioning to "fake" it to give the user a
             * consistent UI.
             */
            '<button style="position: absolute; top: 10px; left: 10px;" class="button" type="submit" name="post_status" value="draft">%s</button>',
            __( 'Save as Draft' )
        );
    }
}

add_action( 'post_submitbox_misc_actions', 'wpse_210259_revert_to_draft_button' );