Sorry for the late response. a lot need to be caught up after the vacation.
I just tried awstats with authentication realm on FreeBSD 4.11, works fine.
Please turn on debug logging by setting "Debug Level" to "HIGH", then check your error.log. it should tell you what happened. Pay attention the warning and error messages at server startup.
Maybe there is something wrong with your htpasswd file, please check the permission. And you can try the realm on other context as well.