Yes, that is indeed a problem, as the cookies that contain your login data either is for the www or the non-www version. While both is the same website, the cookie only works for the one you logged in once.
However, the non www-version does redirect you properly now to the www-version (including the full query string, to prevent problems with links scattered all over the net :P)

The problem also seems to be that both URLs (with and without the www) can be used interchangably. I tend to get logged out whenever I'm on http://www.ao-universe.com and click a site-internal link to http://ao-universe.com .

Sounds like a cookie-problem after all.
Please check your browsers security settings, and allow cookies for this website. If this is ok, please logout, then remove all cookies of this website, and login again.
Depending on your browser, you gotta look where the cookies are stored. Name of cookies should start with [i]ao-universe.com[/i] or [i]www.ao-universe.com[/i].

Am I the only one having problems with the site not remembering me when I return? It was working until the new news page layout and forum New Post count changes, but now every time I come back, I have to log in again. If it was only happening at work, I would chalk it up to our lovely IT department's locked down IE settings, but I'm having the same problem at home as well.