A nit to pick here: Google releases Chrome, not Chromium. We only provide Chromium as a source repository, not binaries. Other independent entities (such as Linux distros) can provide releases of Chromium, but Google does not.

That said, Google doesn't support previous releases for security reasons. We are constantly improving the security profile of Chrome, and hackers (both black hat and white hat) are constantly finding exploits in older versions. (The same is true for all the other major browsers on the market.)

If you want to use Chrome on a previous/older release, please don't. If you want to use Chromium on a previous/older release, also please don't, but you can compile it yourself if you're so inclined.

And for the most part, no, customers don't demand stable old releases of Chrome. They've learned how bad of a security and usability mistake that is from IE6, and they don't want to repeat past mistakes any more than we do.