Not allowing new registrations would end the "hacker" part of hacker news. Hacking is about being open, sharing information, and ALLOWING OTHERS TO SHARE BACK. To disallow new registrations would be to disallow others to share back, as well as kill the "open-ous" of this site.
In short, what you suggest would kill the site, not save it.
Edit: Or at least make it invite-only.