By default httrack will check for updated versions of the existing files. If
you have a lot of existing files, the check can take a painfully long time.

I had this problem with a large site a couple of years back. At the time I
gave up, but I think you can work around it.

Try changing the --cache option.

Basically, your options are

--cache=0 - don't use a cache (always download from server)
--cache=1 - always use a cache (don't check for update after download)
--cache=2 - update before cache (default behavior)

There is more about the cache on the Users Guide.
<http://www.httrack.com/html/fcguide.html>

I use the command line version of httrack.

Not sure how you set that option from the GUI version.

There is an option called "Store ALL files in cache", but I'm not sure it's
the same thing.

Can you share your project config with us?
Maybe one of the experts can help us?