On my installation the checkbox is visible to enable clean URLs.
When you check it and click Save, it reloads the page with the checkbox no longer checked. Why is this?
FYI you can access the page using the clean URL version: /admin/config/search/clean-urls
Run through this guide to ensure you did every step:
https://drupal.org/getting-started/clean-urls
Make sure AllowOverride All is set in your vhost config. Double check that all of step 3 is set in your config file correctly. I had a similar issue on one of my servers and running through this guide fixed my problem.