So wait, sometimes it works and sometimes it doesn't? Sounds like it's a session persistence problem now.
Try outputting [man]session_id/man somewhere (at the top, middle, wherever) on every page. Once you start a session, that identifier should not change. If it does, it means your session was regenerated and your old data is no longer associated with the current session. This can happen if you type in "mysite.com" but have links that point to "www.mysite.com" since "myste.com" doesn't share the same subdomain as "www.mysite.com".
Could this perhaps be your problem? If so, a common solution is to set the session cookie parameters such that the "host" parameter of the cookie is set to ".mysite.com" (with a leading period), which sets the cookie for all subdomains on your website (as opposed to the default configuration of only setting the cookie for the subdomain of the current request).
EDIT: I just tested submitting the form, clicking a few links before finally going to the quote page, and the values I submitted in the form were being correctly populated in the quote form.
As such, I'm really wondering if it wasn't a subdomain issue as I mentioned above.