Is it possible to protect my site from HTTrack Website Copier or any similar program?
Without setting a max number of HTTP request from users.
No, there's no way to do it. Without setting connection parameter limits, there's even no way to make it relatively difficult. If a legitimate user can access your website, they can copy its contents, and if they can do it normally with a browser, then they can script it.

You might setup User-Agent restrictions, cookie validation, maximum connections, and many other techniques, but none will stop somebody determined to copy your website.
