If there was no credible "business models" for free and open source software, then we would not be having any success stories to talk about in FOSS. But there are hundreds if not thousands of FOSS products out there. It just goes to prove that Open Source works. Granted there are always challenges, but somehow it works and many times with better products than proprietary alternatives.
Just toadd my 2cents..
From the little I know, most of the good (secure, actively maintained and supported) FOSS out there are funded. Either the developers are in full time employment as developers, with the employer recognizing the importance of "giving to the community" (examples - Dovecot, Lusca-cache, Exim) or the developers are getting paid via community efforts (direct donations by the software users to foundations, purchase of CD subscriptions and sale of paraphernalia (FreeBSD is in this category). So funding for the development must be there, somehow otherwise soon you see the project fizzle out.