There is a method for updating posts:

public function update() {
    // Form data validation rules
    // irrelevant for the question suppressed

    $id = $this->input->post('id');

    // Upload image
    $config['upload_path'] = './assets/img/posts';
    $config['allowed_types'] = 'jpg|png';
    $config['max_size'] = '2048';

    $this->load->library('upload', $config);

    $post_image = ''; // set default value to empty
    if (!empty($_FILES['userfile'])) {
        $data = array('upload_data' => $this->upload->data());
        $this->upload->do_upload();
        $post_image = $_FILES['userfile']['name'];
    }
    if ($this->form_validation->run()) {
        // so this will pass empty to update_post if no upload
        $this->Posts_model->update_post($id, $post_image);
        redirect('posts/post/' . $id);
    } else {
        $this->edit($id);
    }
}

// change your

public function update_post($id, $post_image) {
    $data = [
        'title' => $this->input->post('title'),
        'description' => $this->input->post('desc'),
        'content' => $this->input->post('body'),
        'cat_id' => $this->input->post('category')
    ];

    if (!empty($post_image)) {
        // push $post_image to $data only if it's not empty
        $data['post_image'] = $post_image,
    }

    $this->db->where('id', $id);
    // so this will only update other keys and not post_image if $data['post_image'] is not set
    return $this->db->update('posts', $data);
}