Aimy Sitemap v29.0 supports HTTP Authentication during a crawl (PRO Feature).

Basic HTTP Authentication Support (PRO Feature)

As requested by a couple of users, Aimy Sitemap’s crawler now supports HTTP Authentication according to RFC 7617 (“Basic” HTTP Authentication Scheme). This way websites which are still in development and not public yet can be crawled as well, for example to prepare the XML & HTML sitemaps or to use Aimy Sitemap’s link checker.

The feature can be enabled in the "Crawler" tab of Aimy Sitemap's options:
Configuring HTTP Authentication for Aimy Sitemap's crawler