User logs into Dashboard, but viewing the site redirects to login-php

This is a new problem, just started this week – reported in Firefox and Safari, but not in Chrome:

Users can log into the Dashboard, but any attempt to get to the domain-level of the site (i.e. “shivanauts.com”) redirects to login-php.

Users can get to any Pages on the site with no problem (i.e. “shivanauts.com/forum”, etc), but going back to the basic domain – or to the page that’s been selected in the Dashboard as the Front Page – inevitably redirects to login-php.

I’ve disabled plugins, but that didn’t have any effect.

And since it’s a private, user-only site, I guess I’m just hoping for some guesses about what might be happening, or where I could start looking.

Thanks!