Widget Options Not saving

I am trying to create a custom Recent Posts widget that accepts a category, to show only posts in that category. I’m having trouble saving the widget options. I’ve done some debugging and found that in the update function, $new_instance only contains the title options and not via_cat. Here’s the code for form and update:

    /**
     * Back-end widget form.
     *
     * @see WP_Widget::form()
     *
     * @param array $instance Previously saved values from database.
     */
    public function form($instance) {
        /* Set up some default widget settings. */
        $defaults = array( 'title' => '', 'via_cat' => 1);
        $instance = wp_parse_args( (array) $instance, $defaults );


        $cats = get_terms('category');
        $category_data = array();
        foreach ($cats as $cat) {
            $category_data[$cat->term_id] = $cat->name;
        }
?>
<p>
    <label for="<?php echo $this->get_field_id( 'title' ); ?>"><?php _e( 'Title:' ); ?></label>
    <input class="widefat" id="<?php echo $this->get_field_id( 'title' ); ?>" name="<?php echo $this->get_field_name( 'title' ); ?>" type="text" value="<?php echo esc_attr( $instance['title'] ); ?>" />
</p>
<p>
    <label for="<?php echo $this->get_field_id('via_cat'); ?>"><?php _e( 'Category:' ); ?></label>
    <select id="<?php echo $this->get_field_id('via_cat'); ?>" name="<?php echo $this->get_field_id('via_cat'); ?>">
<?php
        foreach ($category_data as $id => $name) {
?>
        <option value="<?php echo $id; ?>"<?php echo $instance['via_cat'] == $id ? ' selected="selected"' : ''; ?>><?php echo $name; ?></option>
<?php
        }
?>
    </select>
</p>
<?php
    }



/**
 * Sanitize widget form values as they are saved.
 *
 * @see WP_Widget::update()
 *
 * @param array $new_instance Values just sent to be saved.
 * @param array $old_instance Previously saved values from database.
 *
 * @return array Updated safe values to be saved.
 */
function update( $new_instance, $old_instance ) {
    $instance = $old_instance;
    $instance['title'] = strip_tags( $new_instance['title'] );
    $instance['via_cat'] = $new_instance['via_cat'];

    return $instance;
}

Any help is appreciated.