You've got to maintain your Drupal site properly, to keep it fast.
Here are some tips on how to optimize your Drupal site:
- Enable caching for your Drupal.
- Optimize your Drupal database.
- If your Drupal is hosted on a dedicated solution, you can modify the global MySQL settings for better performance.
- Check your website using this online tool. It will give you valuable information on what modifications can be made in order to improve its performance.
- Disable/remove all modules/blocks you are not using.
(As read in: kb.siteground.com site)