If the webhost does not support keep-alive, I don't think there is anything you can do to enable it yourself. They are most likely not allowing it to be overridden.
I think keep-alive is nice to have, but less of an impact compared to some of the key practices like gzip compression, proper caching, and reducing the number of HTTP requests.
In your case if the need for keep-alive was significantly important, you could consider switching web hosts.