Super-Cache mode not work with http-authorization

Hello!

I have a corporate site with a basiс http-authorization. When I enable super-cache, no pages are cached (i can see it on cache statistic tab). Even if I run super-cache update manually, no reaction. But if I disable http-auth, this mode works fine. This problem is actual with any combination of basic settings (mod_rewrite caching or php caching, cache compression, etc.)

However, legacy-cache (wp-cache) works with http-auth. I was forced to enable it instead of super-cache.

There is a way to solve this problem?

Thanks

https://www.ads-software.com/plugins/wp-super-cache/